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Babita travels a certain distance at a speed of 11 km/hr and double the earlier distance at 44 km/hr. She then returns to the starting point through the same route. If her average speed for the entire journey is 34 km/hr, then what is her speed (in km/hr) for the return journey?

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  1. 79
  2. 76.8
  3. 70
  4. 74.8

Answer (Detailed Solution Below)

Option 4 : 74.8
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Detailed Solution

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Given:

Babita travels distance x at 11 km/h

Then 2x at 44 km/h

Average speed for full journey (6x) = 34 km/h

Formula used:

Average speed = Total distance / Total time

Calculation:

Time for x at 11 km/h = x ÷ 11

Time for 2x at 44 km/h = 2x ÷ 44 = x ÷ 22

Total time for going = x ÷ 11 + x ÷ 22 = 3x ÷ 22

Total distance of full journey = 3x + 3x = 6x

Total time = 6x ÷ 34 = 3x ÷ 17

Time for return = Total time − time for going ⇒ 3x ÷ 17 − 3x ÷ 22

LCM of 17 and 22 = 374

⇒ Time for return = (66x − 51x) ÷ 374 = 15x ÷ 374

Return distance = 3x

Return speed = 3x ÷ (15x ÷ 374) = 3x × 374 ÷ 15x ⇒ 1122 ÷ 15 = 74.8 km/h

∴ The speed of return journey is \(74.8\ km/hr\).

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