Bob left home, riding his bike at a rate of 10mph to go to the lake. cheryl, his wife, left 45 minutes ( 0.75 hour) later, driving her car at a rate of 25mph. how long will it take cheryl to catch up to bob?

30 minutes

Step-by-step explanation:

Let's find how much Bob had covered before Cheryl left.

We need to find Bob's distance in 45 minutes (0.75 hour).

We know D = RT, where D is distance, R is rate, T is time. So,

D = RT

D = 10(0.75) = 7.5 miles

Bob was ahead by 7.5 miles before his wife started.

Now, Bob's rate is 10mph and Cheryl's is 25 mph, that means Cheryl goes 15 miles per hour faster to catch up.

Since, Cheryl will catch up at 15 miles an hour, how long would Cheryl need to catch up 7.5 miles??

Easy!

7.5 is HALF of 15, so Cheryl will required HALF of an hour to catch up, or 30 minutes

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step-by-step explanation: