Question 1122045: Hi
At 1pm a motorist left X travelling to Y at a uniform speed. Two hours later a bus driver started from X along the same road. The bus overtook the motorist at 6pm. The speed of the bus driver was 30kmper hour faster than the motorist.
Find the speed of the motorist.
Find the distance between X and Y if the bus was 60km from Y at 6pm.
thanks
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
At 1 pm a motorist left X travelling to Y at a uniform speed. Two hours later a bus driver started from X along the same road.
The bus overtook the motorist at 6 pm. The speed of the bus driver was 30 km per hour faster than the motorist.
Find the speed of the motorist.
Find the distance between X and Y if the bus was 60km from Y at 6pm.
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The motorist spent 5 hours on the way from the start moment at 1 pm to catching moment at 6 pm.
The bus spent 2 hours less, i.e. only 3 hours from the start to the catching moment.
Both traveled the same distance, which gives you an equation
5*x = 3*(x+30),
where x is the motorist speed (in kilometers per hour) and (x+30) is the bus speed.
Solve the equation
5x = 3x + 90
3x - 3x = 90
2x = 90 ====> x =  = 45.
Thus the motorist speed is 45 km/k. The bus speed is 45 + 30 = 75 km/h.
The bus traveled 3*75 = 225 kilometer.
The distance from X to Y is 225 + 60 = 285 kilometers.
Answer. The motorist speed was 45 kilometers per hour.
The distance from X to Y is 285 kilometers.
Solved.
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- Travel and Distance problems
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- Travel and Distance problems for two bodies moving in the same direction (catching up)
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Be aware : The solution and the answer by @josgarithmetic are both W R O N G.
For your safety, simply ignore it.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Hi
At 1pm a motorist left X travelling to Y at a uniform speed. Two hours later a bus driver started from X along the same road. The bus overtook the motorist at 6pm. The speed of the bus driver was 30kmper hour faster than the motorist.
Find the speed of the motorist.
Find the distance between X and Y if the bus was 60km from Y at 6pm.
thanks
Let motorist’s speed be S
Then bus’ speed = S + 30
Motorist’s and bus’ time to get to meeting-point: 5 and 3 hours, respectively
We then get the following DISTANCE equation: 5S = 3(S + 30)
5S = 3S + 90
5S – 3S = 90
2S = 90
S, or motorist’s speed = 
Distance from X to meeting-point: 5(45), or 3(45 + 30) = 225 km
Therefore, distance from X to Y = 
IGNORE all other INCORRECT or otherwise RUBBISH-ANSWERS!!
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