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Answer:
35.the distance covered by speed of 45 km per hour is 180 km and the the speed of 60 km per hour is 300 km.
35.
Let the man could travel x distance (in km) with a speed of 60 km/h. Since the total distance is 480 km, the remaining 480 - x distance is covered by the man at 45 km/h. And the part of the trip covered by the man at 60 km/h will be x / 480. We have to find this.
The time taken for the man to travel x kilometres in 60 km/h is x / 60 hours and that taken for him to travel 480 - x kilometres in 45 km/h is (480 - x) / 45 hours.
Given that the total time taken for the man to travel 480 km is 9 hours. Thus,
(x / 60) + ((480 - x) / 45) = 9
(3x / 180) + ((1920 - 4x) / 180) = 9
(3x + 1920 - 4x) / 180 = 9
1920 - x = 1620
x = 300 km
So the man covered 300 km at 60 km/h and 180 km in 45 km/h.
Then, the part of the trip covered at 60 km/h is 300 / 480 = 5/8.
36.
Let the distance between the two towns A and B be x (we have to find x, in km). So the distance travelled from A to B by the motorist is the same as that travelled in return from B to A, i.e., x kilometres.
The time taken by the motorist to travel from A to B at 54 km/h is x / 54 hours.
The time taken by the motorist to return from B to A at 60 km/h is x / 60 hours.
Given, the total time taken by the motorist is 9 and 1/2 hours, i.e., 19 / 2 hours. So,
(x / 54) + (x / 60) = 19 / 2
(x / (6 × 9)) + (x / (6 × 10)) = 19 / 2
x [(1 / 9) + (1 / 10)] / 6 = 19 / 2
19 x / 90 = 57
x = 270 km
Hence the distance between the two towns A and B is 270 km.