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?
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.
+130071 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
