SOLUTION: An automobile can travel 200 kilometers in the same time that a truck can travel 150 kilometers. If an automobile travels at a speed of 15 kph faster than the truck, what is the sp

Question 985002: An automobile can travel 200 kilometers in the same time that a truck can travel 150 kilometers. If an automobile travels at a speed of 15 kph faster than the truck, what is the speed of the automobile?

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
An automobile can travel D kilometers in the same time t that a truck can travel d kilometers.
If an automobile travels at a speed of p kph faster than the truck,
what is the speed of the automobile?

R, car speed
r, truck speed
R=r+p

VARIABLES ASSIGNED

VARIABLES UNKNOWN
t, time of each vehicle
R and r

speed time distance CAR r+p t D TRUCK r t d

The question means, what is R?

The tabulated data gives this system:

Solve the system for r and t. This will require a few algebraic steps. Use the value result
of r to evaluate R.

Substitute for t in either equation, the "d" equation being arbitrary choice here.

------substitute the values given and evaluate r, and then use this
to evaluate R.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

An automobile can travel 200 kilometers in the same time that a truck can travel 150 kilometers. If an automobile travels at a speed of 15 kph faster than the truck, what is the speed of the automobile?

Let auto's speed be S
Then truck's speed is: S - 15
Time auto takes to travel 200 km:
Time truck takes to travel 150 km:
Since times are the same, we get:

200(S - 15) = 150S ----- Cross-multiplying
200S - 3,000 = 150S
200S - 150S - 3,000
50S = 3,000
S, or auto's speed = , or km/h
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