Solve.
-A cruise boat travels 96 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.
A)8 mph
B)32 mph
C)56 mph
D)24 mph

Question

Quizplus · Accepted Answer

Let's assume the speed of the boat in still water is 'B' and the speed of the stream is 'S'.

When the boat travels downstream, the effective speed of the boat will be (B + S), and when it travels upstream, the effective speed of the boat will be (B - S).

According to the problem,

Distance downstream = 96 miles 
Time taken downstream = 3 hours 
Therefore, (B + S) = 96/3 = 32

Distance upstream = 96 miles 
Time taken upstream = 6 hours 
Therefore, (B - S) = 96/6 = 16

Now, we can solve these two equations simultaneously to find the values of 'B' and 'S'.

Adding the two equations:
(B+S) + (B-S) = 32 + 16
2B = 48
B = 24 mph

Substituting the value of 'B' in one of the equations:
(B+S) = 32
24 + S = 32
S = 8 mph

Therefore, the speed of the stream is 8 mph. So, the correct answer is (A). Let's assume the speed of the boat is "B" and the speed of the stream is "S".
When the boat travels downstream, its effective speed is increased due to the stream. So its speed can be given by the formula,
Speed downstream = B + S
Similarly, when the boat travels upstream, its effective speed is decreased due to the stream. So its speed can be given by the formula,
Speed upstream = B - S

According to the problem,
Distance downstream = Distance upstream = 96 miles
Time taken downstream = 3 hours
Time taken upstream = 6 hours

Using the formula, Distance = Speed × Time,
We can write,
Speed downstream × Time taken downstream = Distance downstream
(B + S) × 3 = 96
Speed upstream × Time taken upstream = Distance upstream
(B - S) × 6 = 96

Solving these two equations, we get,
B + S = 32            ---(1)
B - S = 16            ---(2)

Adding equation 1 and equation 2, we get,
2B = 48
B = 24

Substituting B = 24 in equation 1, we get,
24 + S = 32
S = 8

Hence, the speed of the stream is 8 mph.

Solve. -A Cruise Boat Travels 96 Miles Downstream in 3 Hours