Arithmetic

Time, Speed & Distance

Medium

A boy travels between point A and point B at a speed of 6 km/h and returns at a speed of 9 km/h. If the total time taken by him is 1 hour 15 min, the distance between A and B is:

6.5 km

5.5 km

4.5 km

9 km

✅ Correct Option: 3

The boy travels from A to B at 6 km/h and returns at 9 km/h. The total time taken is 1 hour 15 minutes.

Convert 1 hour 15 minutes to hours:

$1 + \frac{15}{60} = 1.25$ hours

Let the distance between A and B be $d$ km.

Time taken to go from A to B:

$\frac{d}{6}$ hours

Time taken to return from B to A:

$\frac{d}{9}$ hours

Total time:

$\frac{d}{6} + \frac{d}{9} = 1.25$

The LCM of 6 and 9 is 18.

$\frac{d}{6} = \frac{3d}{18}$

$\frac{d}{9} = \frac{2d}{18}$

$\frac{3d}{18} + \frac{2d}{18} = 1.25$

$\frac{5d}{18} = 1.25$

$5d = 1.25 \times 18$

$5d = 22.5$

$d = \frac{22.5}{5}$

$d = 4.5$

Therefore, the distance between A and B is 4.5 km.

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A boy travels between point A and point B at a speed of 6 km/h and returns at a speed of 9 km/h. If the total time taken by him is 1 hour 15 min, the distance between A and B is:

Solution

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