SOLUTION: an automobile travels at a uniform rate. If the rate were 5 kilometers per hour faster, the distance traveled in 9 hours would be 50 kilometers more than the distance traveled in 1

An automobile travels at a uniform rate. If the rate were 5 kilometers per hour faster, the distance traveled in 9 hours would be 50 kilometers more than the distance traveled in 11 hours at the rate of 5 kilometers per hour less than the actual rate. Find the actual rate.

Ans:

Let the actual rate be x kph

If the rate is 5 kph faster, it is (x+5) kph

At the faster rate, distance travelled in 9 hours = 9*(x+5) = 9*x + 45

If the rate is 5 kph slower, it is (x-5) kph

At the slower rate, distance travelled in 11 hours = 11*(x-5) = 11*x - 55

It is given that the first distance (faster rate) is 50 km more than the second (slower rate).

We get the equation



Simplifying

 or 

Actual speed =  kmph

Check for correctness:

At 5 kph higher speed, i.e. 30 kph, distance in 9 hours = 9 * 30 = 270

At 5 kph slower speed, i.e. 20 kph, distance in 11 hours = 11 * 20 = 220

270 - 220 = 50. So the answer is correct.

:)