SOLUTION: A car and a bus set out at 2pm from the same point headed in the same direction the average speed of the ca r is 30 mph slower than twice the speed of the bus. In two hours, the ca

Question 921633: A car and a bus set out at 2pm from the same point headed in the same direction the average speed of the ca r is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus what is the speed of the car?
What i have done:
Suppose the speed of the bus is x. Then the speed of the car will be 2x-30.
We need to find speed so speed=Distance/Time.
Please help me after that as i am not able to proceed further.
The options are a)40mph b)50mph c)60mph d)70mph
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
Your variable description for speeds of car and bus are inconvenient. Set r as the unknown speed of the bus. The speed then for the car is , or 2r-30 for the car. The car is going faster than the bus.

__________________speeds__________time__________distance
CAR_______________2r-30___________2_____________
BUS_________________r_____________2______________

The distance difference described makes for .
Solve for r, which is the SPEED of the BUS.
Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

A car and a bus set out at 2pm from the same point headed in the same direction the average speed of the ca r is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus what is the speed of the car?
What i have done:
Suppose the speed of the bus is x. Then the speed of the car will be 2x-30.
We need to find speed so speed=Distance/Time.
Please help me after that as i am not able to proceed further.
The options are a)40mph b)50mph c)60mph d)70mph

Let speed of bus be S (You have this as x)
Then speed of car = 2S � 30 (You have this as 2x � 30)
In 2 hours, the bus has traveled a distance of: 2S
In 2 hours, the car has traveled a distance of: 2(2S � 30), or 4S � 60
Therefore, we get: 2S + 20 = 4S � 60
2S � 4S = - 60 � 20
� 2S = - 80
S, or speed of bus = , or 40 mph
Speed of car: 2(40) � 30, or 80 � 30, or mph (CHOICE b)
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