SOLUTION: Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal at the airport. The first shuttle that arrives only has room for one more passenger, so St

Algebra ->  Length-and-distance -> SOLUTION: Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal at the airport. The first shuttle that arrives only has room for one more passenger, so St      Log On


   

Question 628378: Stephanie and her friend, Paula, are waiting for a shuttle to take them to their terminal at the airport. The first shuttle that arrives only has room for one more passenger, so Stephanie gets on. The next shuttle arrives 10 minutes later and Paula gets on. If Stephanie's shuttle travels at a speed of 26 mph and Paula's shuttle travels at a speed of 32 mph, how long will it take Paula's shuttle to catch up to Stephanie's shuttle?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Stephanie and her friend, Paula, are waiting for a shuttle to take them to
their terminal at the airport.
The first shuttle that arrives only has room for one more passenger, so
Stephanie gets on.
The next shuttle arrives 10 minutes later and Paula gets on.
If Stephanie's shuttle travels at a speed of 26 mph and Paula's shuttle
travels at a speed of 32 mph, how long will it take Paula's shuttle to
catch up to Stephanie's shuttle?
:
Change 10 min to 1%2F6 hr
:
Let t = travel time of the 2nd shuttle to catch the first
Let (t+1%2F6) = travel time of the 1st shuttle
:
When the 2nd catches the 1st, they will have traveled the same distance
Write a distance equation: dist = speed * time
:
32t = 26(t+1%2F6)
32t = 26t + 26%2F6
32t - 26t = 26%2F6
6t = 26%2F6
multiply both sides by 6 to get rid of the fraction
6(6t) = 26
36t = 26
t = 26/36
t = 13/18 * 60 = 431%2F3 min to catch the 1st shuttle