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Question

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A. 45 mph

B. 43 mph

C. 40 mph

D. 35 mph

Answer

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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