Alex's bike ride to work usually takes 22 minutes at 9 kph. 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?
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Answer:
Alex should cycle at a speed of **13.2 kph** to reach home by an additional 2 minutes earlier if he decides to use this new route again.
Step-by-step explanation:
Let's start by calculating the time it takes Alex to get to work using his new bike route.
If his usual bike ride takes 22 minutes at 9 kph, then he travels a distance of 22/60 * 9 = 3.3 km.
Since he found a new bike route that was 5 minutes faster, then his new bike ride takes 22 - 5 = 17 minutes.
To calculate his new speed, we can use the formula:
`distance = speed * time`
where distance is the same for both bike rides.
So we have:
`3.3 = 9 * (22/60)`
`3.3 = 3.3`
and
`3.3 = speed * (17/60 - 2/60)`
Simplifying this equation gives:
`speed = distance / time`
`speed = 3.3 / (15/60)`
`speed = 13.2 kph`
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