Question 894066: The distance between two cities A and B is 300 km. A car leaves city A towards B at a constant speed of 80 km/hr. At the same time, a car leaves city B towards A at a constant speed of 70 km/hr. When will the two cars meet?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the cars will meet in 2 hours.
the first car travels 80 kmph for T hours to go a distance of x.
the second car travels 70 kmph for T hours to go a distance of 300 - x.
x and 300 - x are where the cars meet.
for example, if the first car travels 100 km and the second car travels 200 km, they will meet at the point where the first car is 100 km from it's starting point and the second car is 200 km from its starting point.
the total distance traveled by both cars is 300 km.
since T will be the same for both cars, we solve for T.
the first car formula is 80 * T = x
solve for T to get T = x/80.
the second car formula is 70 * T = 300 - x
solve for T to get T = (300 - x)/70
since they are both equal to T then they are both equal to each other and you get:
x/80 = (300 - x)/70
solve for x to get x = 160
this means that 300 - x = 140.
now we can solve for T.
T in both equations will be the same.
for the first equation 80 * T = x becomes 80 * T = 160 which makes T = 2.
for the second equation 70 * T = 300 - x becomes 70 * T = 300 - 160 = 140.
70 * T = 140 yields T = 2 again.
they will meet in 2 hours.
the first car will have traveled 160 km.
the second car will have traveled 140 km.
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