Question

A car drives a distance of d miles at 30 mph and returns at 60 mph. What is its average rate of the round trip?
A. 45 mph
B. 43 mph
C. 40 mph
D. 35 mph

Answer 1

Hint: In this question, first of all, assume that the car reached a certain point and then return by taking a time of \[{t_1}\] and \[{t_2}\] hours respectively. Then find the total time is taken and the total distance covered to complete the round trip by the car to calculate the average speed. So, use this concept to reach the solution to the given problem.

Complete step-by-step solution:
Given that
The distance travelled by the car = d miles
Speed of the car to reach a certain point = 30 mph
Speed of the car where it returns from that point = 60 mph
We know that \[{\text{time}} = \dfrac{{{\text{distance}}}}{{{\text{speed}}}}\].
Let \[{t_1}\] be the time taken to reach the point. So, we have \[{t_1} = \dfrac{d}{{30}}\]
Let \[{t_2}\] be the time taken to return from that point. So, we have \[{t_2} = \dfrac{d}{{60}}\]
The total time taken to reach and to return to a certain point is \[t = {t_1} + {t_2} = \dfrac{d}{{30}} + \dfrac{d}{{60}} = \dfrac{{2d + d}}{{60}} = \dfrac{d}{{20}}\]
The total distance covered to reach and to return to the certain point is \[D = d + d = 2d\]
We know that \[{\text{average speed}} = \dfrac{{{\text{total distance covered}}}}{{{\text{total time taken}}}}\]
So, the average speed for the total trip \[ = \dfrac{D}{t} = \dfrac{{2d}}{{\dfrac{d}{{20}}}} = \dfrac{{2 \times 20 \times d}}{d} = 40{\text{ mph}}\]
There, the average speed in the total trip = 40 mph

Thus, the correct option is C. 40 mph

Note: Average speed is calculated by dividing the total distance that something has traveled by the amount of time it took it to travel that distance. Here we have used speed-distance-time formula i.e., \[{\text{speed}} = \dfrac{{{\text{distance}}}}{{{\text{time}}}}\] to calculate the individual times taken to reach the point and to return the point in the whole trip.