SOLUTION: The distance between two cities A and B is 140 km. A car driving from A to B left at the same time as a car driving from B to A. The cars met after one hour, then the first car rea

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Question 1028084: The distance between two cities A and B is 140 km. A car driving from A to B left at the same time as a car driving from B to A. The cars met after one hour, then the first car reached city B 35 minutes later than the second car reached city A. Find the speed of each car.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let car from A meet at C after d km
It took 1 hour
so speed of car A = d km/h
Speed of car B will be (140-d)
The distance car B has to travel is D km
The distance car A has to travel is (140-d)
time carA - time car B to reach the opposite end = 35 minutes
(140-d)/d - d/(140-d) = 7/12
((140-d)^2 -d^2)/d(140-d) = 7/12
19600 -280d+d^2-d^2= 7d(140-d)/12
19600-280d = (980d -7d^2)/12
235200-3360d=980d-7d^2
7d^2-4340d+235200=0
Find the roots of the equation by quadratic formula

a= 7 b= -4340 c= 235200

b^2-4ac= 18835600 - 6585600
b^2-4ac= 12250000 sqrt%28%0912250000%09%29= 3500
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 )/
x1=( 4340 + 3500 )/ 14
x1= 560
x2=( 4340 - 3500 )/ 14
x2= 60
Ignore value 560
speed of car A 60 km/h
speed of car B =80 km/h