JAMB 2023 Mathematics · Question 64

A student pilot was required to fly to an airport and then return as part of his flight training. The average…

Question

A student pilot was required to fly to an airport and then return as part of his flight training. The average speed to the airport was 120 km/h, and the average speed returning was 150 km/h. If the total flight time was 3 hours, calculate the distance between the two airports.

A.270 km
B.200 km
C.360 km
D.450 km

Answer: B. 200 km

Explanation written with AI and checked against the answer key

1. Analyze the Question

We are given:

Speed to the airport ( $v_1$ ) = $120\text{ km/h}$
Speed returning ( $v_2$ ) = $150\text{ km/h}$
Total time ( $T$ ) = $3\text{ hours}$
Distance ( $d$ ) is the same for both legs of the trip.

We need to find the distance $d$ .

2. Explain the Concept

The fundamental formula for motion is:

\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Since the total time is the sum of the time taken to go ( $t_1$ ) and the time taken to return ( $t_2$ ), we can write:

t_1 + t_2 = T

\frac{d}{v_1} + \frac{d}{v_2} = T

3. Show the Solution

Substitute the given values into the equation:

\frac{d}{120} + \frac{d}{150} = 3

To solve for $d$ , find the Least Common Multiple (LCM) of 120 and 150, which is 600. Multiply every term by 600 to clear the fractions:

600 \left( \frac{d}{120} \right) + 600 \left( \frac{d}{150} \right) = 600(3)

Simplify:

5d + 4d = 1800

9d = 1800

Divide both sides by 9:

d = \frac{1800}{9}

d = 200\text{ km}

4. Identify the Answer

The distance between the two airports is 200 km. This corresponds to option B.

5. Exam Tip

When you have a round trip with two different speeds ( $v_1$ and $v_2$ ) and a total time ( $T$ ), you can use the shortcut formula:

d = \frac{v_1 \times v_2}{v_1 + v_2} \times T

Plugging in our values:

d = \frac{120 \times 150}{120 + 150} \times 3 = \frac{18000}{270} \times 3 = \frac{18000}{90} = 200\text{ km}

This formula is a great time-saver for JAMB!

AI can make mistakes. Report anything that looks wrong.