Nick wants to travel from city A to city B. If he rides a motorcycle for 12 hours then change to bicycle and ride for 9 hours, he will reach city B in time. If he rides bicycle for 21 hours then change to motorcycle and ride for 8 hours, he will reach city B in time also. How long will it take if he rides motorcycle for the whole journey?
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1 Answer

m=motorcycle speed; b=bicycle speed.

Distance=speed×time=AB=12m+9b=21b+8m=tb where t is the time to do the whole journey by bicycle.

Therefore 4m=12b, m=3b; 8m=24b; 21b+24b=tb; 45b=tb, 45=t. It takes 45 hours.

 

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