The interstate on-ramp is 5.5 km west of your home, and on leaving for grandmother's house you are only able to accomplish an average velocity of 38 km/hr between your home and the on-ramp. At the on-ramp, you wait for traffic for 2.0 min before proceeding toward grandmother's house. If you wish to arrive there, which is 15 km south of the on-ramp, over a river and through some woods, having achieved an average velocity of 42 km/hr for the whole trip, how fast do you need to drive south on the interstate highway?
A) 58 km/hr
B) 48 km/hr
C) 74 km/hr
D) 39 km/hr

Question

Quizplus · Accepted Answer

We can use the equation:

average velocity = total distance / total time

Let's calculate the total distance of the trip first:

distance from home to on-ramp = 5.5 km
distance from on-ramp to grandmother's house = 15 km

total distance = 5.5 km + 15 km = 20.5 km

Let's calculate the total time of the trip now:

time from home to on-ramp = distance / velocity = 5.5 km / 38 km/hr = 0.145 hours
time waiting at on-ramp = 2.0 min = 0.033 hours
time from on-ramp to grandmother's house = distance / velocity = 15 km / 42 km/hr = 0.357 hours

total time = 0.145 hours + 0.033 hours + 0.357 hours = 0.535 hours

Now we can use the equation to find the needed average velocity for the whole trip:

average velocity = total distance / total time = 20.5 km / 0.535 hours = 38.3 km/hr

Since the average velocity for the whole trip needs to be 42 km/hr, the required velocity for the interstate highway segment would be:

velocity = (required average velocity * total time - time from home to on-ramp * velocity from home to on-ramp) / time from on-ramp to grandmother's house

velocity = (42 km/hr * 0.535 hours - 0.145 hours * 38 km/hr) / 0.357 hours

velocity = 74 km/hr

Therefore, the answer is C: 74 km/hr.

The Interstate On-Ramp Is 5