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Question

A cyclist covered a distance of 96 km two hours faster than he assumed. Every hour he travelled 1 km more than he intended to cover in 1 h 15 min. What was his speed?

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Solution

He planned to cover x km in 1hr15min (7560m)(54hr)
He actually covered (x+1) km in every hour.

Planned speed =x54=4x5km/h

Actual speed x+11=x+1km/hr
He reached the 96 km 2 hrs faster than his assumed speed.
964x596x+1=2

120x96x+1=2
120(x+1)96x=2x(x+1)
120x+12096x=2x2+2x
2x222x120=0
x211x60=0
x215x+4x60=0
x(x15)+4(x15)=0
x=15km/hr
Actual speed =x+1=16km/hr

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