A car travels at a constant speed towards a town. If it increases its speed by 15 km/h, the time required is in a ratio of 6 : 5. If it reduces its speed by 15 km/h, it needs another 105 minutes to arrive at the destination. Find the distance travelled by the car.

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  525 km

Step-by-step explanation:

Let d represent the distance to the town. Let s represent the nominal speed of the car. The relation between time, speed, and distance is d = st.

  t1 = d/s

  t2 = d/(s+15)

  t1 : t2 = 6 : 5 . . . increasing the speed reduces the time

Substituting for t1 and t2, we have ...

  (d/s)/(d/(s+15)) = 6/5

  (s +15)/s = 6/5

  1 +15/s = 1 +1/5

  s = 5·15 = 75 . . . . nominal speed in km/h

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Decreasing the speed increases the time.

  d/75 +(105/60) = d/(75-15)

  d(60/75) +105 = d . . . . . . multiply by 60

  105 = d/5 . . . . . . . . . . . subtract 4/5d

  525 = d . . . . . . . . . . multiply by 5

The distance traveled by the car is 525 km.  

answer: answer

step-by-step explanation: