SOLUTION: 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

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Question 1144190: 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?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
rate * time = distance.

rate is in kilometers per hour.
time needs to be in hours.
distance is in kilometers.

22 minutes = 22/60 hours.
22 - 5 = 17 minutes = 17/60 hours.
17 - 2 = 15 minutes = 15/60 hours.

on his original route, he is traveling at 9 kilometers per hour for 22/60 hours.
the distance traveled is 22/60 * 9 = 198/60 kilometers.

on his new route, he is traveling at 9 kilometers per hour for 17/60 hours.
the distance he has traveled is 17/60 * 9 = 153/60 kilometers.

he wants to travel this new route 2 minutes faster.
he needs to know how much faster he has to cycle.
the formula is still rate * time = distance.
the rate is what he wants to find.
the time is 15/60 hours.
the distance is 153/60 kilometers.
the formula becomes rate * 15/60 = 153/60
solve for rate to get rate = 153/60 * 60/15 = 153/15 kilometers per hour.
153/15 = 10.2 kilometers per hour.

that should be your solution.
he is traveling at 10.2 kilometers per hour for 15/60 hours for the new route distance of 15/60 * 10.2 = 153/60 kilometers.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

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?
Since new route takes 5 minutes less, then time using new route = 22  -  5 = 17 mins, or 

Since he apparently biked the same speed on the new route, then new route’s distance = 

To get home 2 minutes earlier, his time on new route must be 17  -  2 = 15 mins, or 

Then, his speed to accomplish this task is:  

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