<PRE><B>Question 712386</B>
a car leaves a town 20 minutes after a bus.
 The speed of the car is 10 kph faster than the bus.
 After traveling 100kms, the car overtakes the bus.
 What is the speed of each vehicle?
:
Let s = bus speed
then
(s+10) = car speed
:
Change 20 min to 1/3 hr
:
When the car overtakes the bus both will have traveled 100 km
:
Write a time equation; time t=dist/speed
Bus time = 20 min + Car time
{{{100/s}}} = {{{1/3}}} + {{{100/(s+10)}}}
multiply by 3s(s+10) resulting in
3(s+10)(100) = s(s+10) + 3s(100)
300s + 3000 = s^2 + 10s + 300s
Arrange as a quadratic equation
0 = s^2 + 10s + 300s - 300s - 3000 
s^2 + 10s - 3000 = 0
Factors to
(s + 60)(s - 50) = 0
The positive solution
s = 50 mph is the bus
then, obviously,
60 mph is the car 
:
:
See if this checks out. Find the travel time of each
100/50 = 2 hrs for the bus
100/60 = 1{{{2/3}}} hrs
------------------------
differ by {{{1/3}}} hr or 20 min

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