Question

Alex’s bike ride to work usually takes 22 minutes. One morning he found a new bike route that was 5 minutes faster. If he decides to use this new route again and wants to reach home by an additional 2 minutes earlier, how fast should he cycle?

Answer 1

Alex has to cycle
`(17)/(15)` times faster.

Explanation:

Let x meters per minute be Alex's initial rate. If Alex’s bike ride to work usually takes 22 minutes, then the distance from home to work is 22x meters.

One morning he found a new bike route that was 5 minutes faster, then he spends 22-5=17 minutes on the way home cycling at the rate x meters per minute. Then the length of the new route is 17x meters.

If he decides to use this new route again and wants to reach home by an additional 2 minutes earlier, then he will spend 17-2=15 minutes to cover 17x meters. So, the new rate will be

`(17x)/(15)\ \text{meters per minute}`

Now,

`((17x)/(15))/(x)=(17)/(15)`

so, Alex has to cycle
`(17)/(15)` times faster.