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A man decides to travel 80 kilometers in 8 hours partly, by foot and partly on a bicycle. If his speed on foot is 8 km/hr and on bicycle 16 km/hr. what distance would he travel on foot?

A man decides to travel 80 kilometers in 8 hours partly, by foot and partly on a bicycle. If his speed on foot is 8 km/hr and on bicycle 16 km/hr. what distance would he travel on foot? Correct Answer 48 km

Given:

A man travel 80 km in = 8 hours

His speed on foot = 8 km/hr

His speed on bicycle = 16 km/hr

Formula:

Speed = Distance/Time

Mixture and Allegation method:

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Where, a > c > b

Calculation:

Short Trick:

Average speed of man = 80/8 = 10 km/hr

Using allegation method

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Time ratio of distance cover with the speed of 8 km/hr to that of 16 km/hr = 6 : 2

⇒ Time taken to cover distance by foot = 6/8 × 8 = 6 hr

∴ Distance covered by on foot = 8 × 6 = 48 km

Detailed method:

Let distance covered on foot be x km

⇒ Distance covered by bicycle = (80 – x) km

According to the question

x/8 + (80 – x)/16 = 8

⇒ (2x + 80 – x)/16 = 8

⇒ x + 80 = 128

⇒ x = 128 – 80

⇒ x = 48 km

∴ Distance covered by foot is 48 km.

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