A delivery van travels from Town A to Town B, a distance of 120\text{ km}, at an average s… — JAMB UTME

A delivery van travels from Town A to Town B, a distance of $120\text{ km}$ , at an average speed of $60\text{ km/h}$ . On the return journey along the same route, traffic congestion reduces its average speed by one-third. What is the average speed of the van for the entire round trip?

$48\text{ km/h}$ Answer
B
$50\text{ km/h}$
C
$30\text{ km/h}$
D
$24\text{ km/h}$

Answer

The average speed for the entire round trip is

48\text{ km/h}

The correct answer is found by dividing the total round-trip distance of

240\text{ km}

by the total journey time of

5\text{ hours}

(

2\text{ hours}

outbound and

3\text{ hours}

return), yielding

48\text{ km/h}

Step-by-Step Solution

Calculate the time taken for the outbound journey.

\text{Time}_{\text{out}} = \frac{120\text{ km}}{60\text{ km/h}} = 2\text{ hours}

Time equals distance divided by speed.

Calculate the return speed and return time.

\text{Return speed} = 60 - \left(\frac{1}{3} \times 60\right) = 40\text{ km/h}. \text{Time}_{\text{return}} = \frac{120\text{ km}}{40\text{ km/h}} = 3\text{ hours}.

Speed reduction of one-third leaves two-thirds of the initial speed.

Compute total distance and total time for the round trip.

\text{Total distance} = 120 + 120 = 240\text{ km}; \text{Total time} = 2 + 3 = 5\text{ hours}.

A round trip covers the distance twice.

Divide total distance by total time to find average speed.

\text{Average speed} = \frac{240\text{ km}}{5\text{ hours}} = 48\text{ km/h}.

Average rate over unequal sub-intervals requires total quantity over total time.

Key Concept

Average Rate for Round-Trip Journeys

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