Question

A motorist left town X at 08 00 for town Y situated 120km away, travelling at a constant speed of v km/hr, so as to arrive at Y at 10 40. But, after travelling for 80 minutes, his car developed engine trouble and he had to stop for 30 minutes to repair it. Then he continued his journey at a speed of u km/hr, so as to arrive at Y at 10 40. a) sketch the distance-time graph for the car. b) Calculate the valued of v and u.

Answer 1

v = 45 km/hr u = 72 km/hr Can't sketch the graph, but can describe it. The Y-axis will be the distance. At the origin it will be 0, and at the highest point it will have the value of 120. The X-axis will be time in minutes. At the origin it will be 0 and at the rightmost point, it will be 160. The graph will consist of 3 line segments. They are 1. A segment from (0,0) to (80,60) 2. A segment from (80,60) to (110,60) 3. A segment from (110,60) to (160,120) The motorist originally intended on driving for 2 2/3 hours to travel 120 km. So divide the distance by the time to get the original intended speed. 120 km / 8/3 = 120 km * 3/8 = 360/8 = 45 km/hr After traveling for 80 minutes (half of the original time allowed), the motorist should be half of the way to the destination, or 120/2 = 60km. Let's verify that. 45 * 4/3 = 180/3 = 60 km. So we have a good cross check that our initial speed was correct. v = 45 km/hr Now having spent 30 minutes fixing the problem, out motorist now has 160-80-30 = 50 minutes available to travel 60 km. So let's divide the distance by time: 60 / 5/6 = 60 * 6/5 = 360/5 = 72 km/hr So the 2nd leg of the trip was at a speed of 72 km/hr

Answer 2

To answer a, it is important that we have the values of v and u first. From 8:00 to 10:40, there are approximately 160 minutes or 2.67 hours.

(1) Travelling v km/h for 80 minutes (4/3 hours)

D = (4/3 v)

(2) Stopped for 30 minutes.

D₂ = (0)(0.5) = 0


(3) Traveled with speed of u for the rest of the trip.

D₃ = (2.67 - 0.5 - 4/3)(u) = 5u/6

Adding up the distances covered,

D = 120 = 4v/3 + 5u/6

Also, as per given,
((8/3)(v)) = 120

v = 45 km/h

From the equation above,
4(45)/3 + (5)(u)/6 = 120

The value of u from the equation is 72 km/h.

(b) v = 45 km/h and u = 72 km/h.

(a) The graph is attached.