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? - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Concept- We’ll assume the time taken by car reached a certain point and then return by taking a time of

t_{1}

and

t_{2}

hours respectively. We’ll use this formula

Time = \frac{distance}{speed}

to calculate time, and

Average speed = \frac{total distance covered}{total time taken}

Distance covered by the car = D miles

We know that,

time = \frac{distance}{speed}

Let

t_{1}

be the time taken to reach the point.

t_{1} = \frac{d}{30}

Let

t_{2}

be the time taken to return the point.

t_{2} = \frac{d}{60}

Let,

t

total time taken to reach and to return to a certain point

t = t_{1} + t_{2}

t = \frac{d}{30} + \frac{d}{60}

t = \frac{2 d + d}{60}

t = \frac{d}{20}

D = d + d

D = 2 d

Average speed = \frac{total distance covered}{total time taken}

So,

Average speed for total trip = \frac{D}{t}

Average speed for total trip = \frac{2 d}{\frac{d}{20}}

Average speed for total trip = \frac{2 \times 20 \times d}{d}

Average speed for total trip = 40 mph

Hence, the correct option is 3.

Related content