Question 1

Solve.
-Jill is 27.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2.5 kilometers per hour. They meet in 5 hours. How fast is Joe walking?

Accepted Answer

Joe is walking at 3 kilometers per hour. Since they meet in 5 hours and Jill walks at 2.5 kilometers per hour, Jill covers 12.5 kilometers (2.5 km/h * 5 h). The total distance is 27.5 kilometers, so Joe covers the remaining 15 kilometers in 5 hours, which means he walks at 3 kilometers per hour (15 km / 5 h).

Question 2

Solve.
-John and Tony start from GraysLake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Accepted Answer

Let Tony's speed be $x$ miles per hour. Then John's speed is $2x$ miles per hour. Let t1 be Tony's time and t2 be John's time. We know that $t2 = t1 - 3$. Using the formula $distance = rate \cdot time$, we have $10 = xt1$ and $10 = 2xt2$. Substituting for $t2$, we get $10 = 2x(t1-3)$. Simplifying gives $t1 = 6$ and $x=5/3$. Therefore, Tony's speed is $5/3$ miles per hour and John's speed is $2\cdot(5/3) = 10/3$ miles per hour. Thus, choice B is correct.

Question 3

Solve.
-A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $21 \mathrm { mph }$, what is the speed of the plane in still air?

Accepted Answer

Let the speed of the plane in still air be $ x $ mph. With the wind, the plane's speed is $ x + 21 $ mph, and against the wind, it is $ x - 21 $ mph. The time taken for both journeys is the same, so $\frac{420}{x + 21} = \frac{350}{x - 21}$. Solving this equation gives $ x = 231 $ mph.

Question 4

Solve.
-A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower than the power boat. Find the speed of each boat.

Accepted Answer

The answer of Solve.
-A cabin cruiser travels 20 miles in...

Question 5

Solve.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 7 miles per hour, and Delvis is traveling at the speed of 4 miles per hour. In 2 hours what is the distance between them?

Accepted Answer

In 2 hours, Candy will have traveled 7 × 2 = 14 miles.
In 2 hours, Delvis will have traveled 4 × 2 = 8 miles.
Therefore, the distance between them is 14 − 8 = 6 miles.

Question 6

Solve.
-An express and local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Accepted Answer

The express travels twice as fast as the local and arrives 1 hour ahead of the local. So, the express's speed is 50 mph and the local's speed is 25 mph.

Question 7

Solve.
-The speed of a stream is $6 \mathrm { mph }$. If a boat travels 68 miles downstream in the same time that it takes to travel 34 miles upstream, what is the speed of the boat in still water?

Accepted Answer

The answer of Solve.
-The speed of a stream is \(6...

Question 8

Solve.
-From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 69 miles apart?

Accepted Answer

The answer of Solve.
-From a point on a river, two...

Question 9

Solve.
-$\begin{array} { l } 
x + y + z = 1 \
x - y + 3 z = - 13 \
5 x + y + z = 9
\end{array}$

Accepted Answer

The answer of Solve.
-\(\begin{array} { l } 
x + y...

Question 10

Solve.
-An airplane travels 800 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Accepted Answer

The speed of the airplane against the wind is $800 \, \text{miles} / 4 \, \text{hours} = 200 \, \text{mph}$, and with the wind is $800 \, \text{miles} / 2 \, \text{hours} = 400 \, \text{mph}$. The wind's rate is the difference between the plane's speed with and without the wind divided by 2, which is $(400 - 200) / 2 = 100 \, \text{mph}$.

Question 11

Solve.
-A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.

Accepted Answer

Let x be the speed of the boat in still water and y be the speed of the stream. Then we have:
x + y = 48/3 = 16 (speed downstream)
x - y = 48/12 = 4 (speed upstream)

Solving for x, we get x = 10 mph. Substituting this value back into either equation, we get y = 6 mph. Therefore, the speed of the stream is 6 mph, which corresponds to choice C.

Quiz 8: Systems of Equations

Solve. -Jill is 27.5 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2.5 kilometers per hour. They meet in 5 hours. How fast is Joe walking?

Solve. -John and Tony start from GraysLake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Solve. -A plane flies 420 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $21 \mathrm { mph }$ , what is the speed of the plane in still air?

Solve. -A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5 mph slower than the power boat. Find the speed of each boat.

Solve. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at the speed of 7 miles per hour, and Delvis is traveling at the speed of 4 miles per hour. In 2 hours what is the distance between them?

Solve. -An express and local train leave GraysLake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Solve. -The speed of a stream is $6 \mathrm { mph }$ . If a boat travels 68 miles downstream in the same time that it takes to travel 34 miles upstream, what is the speed of the boat in still water?

Solve. -From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 13 miles per hour. In how many hours will they be 69 miles apart?

Solve. - $\begin{array} { l } x + y + z = 1 \\x - y + 3 z = - 13 \\5 x + y + z = 9\end{array}$

Solve. -An airplane travels 800 miles against the wind in 4 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Solve. -A cruise boat travels 48 miles downstream in 3 hours and returns to its starting point upstream in 12 hours. Find the speed of the stream.