SOLUTION: I need help with a question: Ben and his friend lives 1300 kilometers away from each other. Ben drives 65 km/h while his friend drives 75 km/h, how long does it take for them to p

Question 263616: I need help with a question:
Ben and his friend lives 1300 kilometers away from each other. Ben drives 65 km/h while his friend drives 75 km/h, how long does it take for them to pass each other? Thanks in advance :)
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Start with the distance equation: d = rt, where d=distance, r=rate, t=time.
d = 1300 km
Ben's rate of speed = 65 km/hr
Friend's rate of speed = 75 km/hr
.
When they pass each other, they will have been driving for the same amount of time and they will have covered the 1300 km, but they will have covered different distances. You can visualize that they are converging at their combined rates of speed or 140 km/hr.
.
What we need to determine is 't'.
75t + 65t = 1300
140t = 1300
t = 1300/140
t = 9.2857143 hrs
.
So, about 9.3 hrs after they both start, they will pass each other going in opposite directions.
.
We can check by substituting the known values in the distance equation for each driver and checking their combined miles driven to the known distance of 1300 km:
Ben drives 65 km/hr * 9.2857143 hr = 603.5713 km
Friend drives 75 km/hr * 9.2857143 hr = 696.4286 km
= 1299.9999 or approximately 1300 km.
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