SOLUTION: A bus averages 6 kilometers an hour less than a passenger car. The bus travels 80 kilometers in the same time that the car travels 112 kilometers. Find the rate of each.

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Question 184851: A bus averages 6 kilometers an hour less than a passenger car. The bus travels 80 kilometers in the same time that the car travels 112 kilometers. Find the rate of each.
Found 4 solutions by HyperBrain, ikleyn, josgarithmetic, greenestamps:
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1:
::
Let x=rate of the passenger car
_ x-6=rate of the bus
::
Note: distance=rate*time so time=distance/rate
::
Step 2: Write the algebraic equation
::
80/(x-6)=120/x
::
Step 3: multiply both sides by x(x-6)
::
80x=120(x-6)
80x=120x-720
40x-720=0
4x-72=0
x=72/4=18 :: Therefore, the passenger car travels at the rate of 18 km/hr.
x-6=18-6=12 :: Therefore, the bus travels 12 km in 1 hr.
::
Power up,
HyperBrain!
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::
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Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
A bus averages 6 kilometers an hour less than a passenger car.
The bus travels 80 kilometers in the same time that the car travels 112 kilometers. Find the rate of each.
~~~~~~~~~~~~~~~~~~~~~~~~~~


        Calculations in the post by @HyperBrain are irrelevant to the given problem, since
        in his calculations, @HyperBrain uses different numbers from the given in the post.
        It leads him to wrong answer.

        I came to bring a correct/adequate solution. 


Step 1:

Let x be the rate of the passenger car
    Then x-6 is the rate of the bus

Note: distance=rate*time so time=distance/rate


Step 2: Write the algebraic equation

80/(x-6) = 112/x


Step 3: multiply both sides by x(x-6)

80x = 112(x-6)
80x = 112x-672
32x = 672
x = 672/32 = 21   Therefore, the passenger car travels at the rate of 21 km/hr.
x-6 = 21-6 = 15   Therefore, the bus travels 15 km in 1 hr.


CHECK for the travel time: 80%2F15 = 51%2F3  hours.

                           112%2F21 = 51%2F3 hours, the same time.

                           Precisely correct !

Solved correctly.


//////////////////////////////////


The fact that @HyperBrain repeats these words "Power up, @HyperBrain!" from post to post,
tells me that he uses a computer code.

The fact that @HyperBrain makes numerous errors of the same type from post to post,
tells me that his computer code is erroneous and incorrectly reads the input data.



Answer by josgarithmetic(39835) About Me  (Show Source):
You can put this solution on YOUR website!
            SPEEDS      IME                 DISTANCES

BUS           b         80/b                180

CAR         b+6        112/(b+6)             112

80%2Fb=112%2F%28b%2B6%29

80%28b%2B6%29=112b
10%28b%2B6%29=14b
5%28b%2B6%29=7b
5b%2B30=7b
30=2b
highlight%28b=15%29-------speed of the bus.
Car goes 21 kilometers per hour.

Answer by greenestamps(13364) About Me  (Show Source):
You can put this solution on YOUR website!


In the same amount of time, the difference in distances traveled is 32 km and the difference in speeds is 6 km/hr. That means the number of hours that both vehicles traveled is 32/6 = 16/3.

Then the speed of the bus is (80)/(16/3) = 15 km/hr and the speed of the car is (112)/(16/3) = 21 km/hr.

ANSWERS:
bus 15km/h
car 21km/h