Question 1119548: Alex and Bert Agreed to meet on the highway connecting their hometowns, which are 120 km apart. Alex drives at 45 kph, while bert drives at 35 kph. In how many hours will they meet?
Found 3 solutions by Theo, MathTherapy, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! they are 120 km apart.
alex drives at 45 kmph.
bert drives at 35 kmph.
if alex drives x km, then they will meet when bert drives (120 - x) km.
they will both have been driving the same amount of time.
the formula to use is R * T = D
R is the rate in kilometers per hour.
T is the time in hours.
D is the distance in kilometers.
for alex, the formula becomes 45 * T = x
for bert, the formula becomes 35 * T 120 - x
these 2 equations need to be solved simultaneously.
one way to solve is as follows:
rearrange the terms so all the variables are on one side of the equations and all the constants are on the other side.
the equations become:
45 * T - x = 0
35 * T + x = 120
add the second equation to the first to get:
80 * T = 120
solve for T to get T = 120/80 = 12/8 = 1.5 hours.
they both travel for 1.5 hours.
in that 1.5 hours, alex travels 45 * 1.5 = 67.5 kilometers.
in the same 1.5 hours, bert travels 35 * 1.5 = 52.5 kilometers.
the sum of 67.5 and 52.5 = 120 kilometers in total.
if alex started at the 0 kilometer mark, then he traveled 0 + 67.5 kilometers to the 67.5 kilometer mark in 1.5 hours.
if bert started at the 120 kilometer mark, then he traveled 120 - 52.5 kilometers to the 67.5 kilometer mark in 1.5 hours.
they met at the 67.5 kilometer mark.
the solution is that they will meet in 1.5 hours.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Alex and Bert Agreed to meet on the highway connecting their hometowns, which are 120 km apart. Alex drives at 45 kph, while bert drives at 35 kph. In how many hours will they meet?
It needs to be pointed out that they left their respective destinations at the SAME TIME. It's safe to assume that
they did, and if so, and with the time they took to meet being T, we get the following DISTANCE equation: 45T + 35T = 120.
Solve this for the time it'll take them to meet.
Answer by Alan3354(69443)  (Show Source):
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