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# At 7:18 you get on the bus and are off to school. The bus travels at 42mph. Fifteen minutes later your mother realized you left your math pr

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At 7:18 you get on the bus and are off to school. The bus travels at 42mph. Fifteen minutes later your mother realized you left your math project on the kitchen table. She drives 72mph to catch up with the bus. What time will your mom catch up with the bus?

Guest Oct 14, 2017
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#1
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Let the time taken by the bus =T

Then the time taken by the Mom =T - 15

Distance  =Time x Speed

42T =72(T - 15)

42T =72T - 1,080

42T - 72T = -1,080

-30T = -1,080

T = -1,080 / -30

T = 36 minutes taken by the bus

36 - 15 =21 minutes taken by the Mom.

7:18 + :36 =7:54 am - when the Mom catches up with the bus.

Guest Oct 14, 2017
edited by Guest  Oct 14, 2017
#2
+82538
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The distance that the bus travels each minute is  42/60 miles.....and it has a 15 minute head start

So....in 15 minutes....the distance that your mother will have to close to catch the bus is

(15) * 42/60  miles

The distance that your mother travels each minute is 72/60 miles

So......the time it will take to catch the bus is given by

( 72/60 - 42/60) T  = 15 * 42 / 60

(30/60)T = 15* 42 .60      multiply through by 60

30T   =  15*42   divide both sides by 30

T = (1/2) 42

T  = 21  minutes

So.....15 minutes after 7:18 AM is 7:33AM....and 21 minutes after this is 7:54 AM....and this is when she will overtake the bus

CPhill  Oct 14, 2017
edited by CPhill  Oct 14, 2017

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