SOLUTION: A motorist travelled x hours at an average speed of 40km/h and continued for y hours at an average of 30km/h. Altogether, he travelled 470km/h in 13 hours. Find the value of x and
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Question 1151614: A motorist travelled x hours at an average speed of 40km/h and continued for y hours at an average of 30km/h. Altogether, he travelled 470km/h in 13 hours. Find the value of x and y Found 2 solutions by greenestamps, ikleyn:Answer by greenestamps(13200) (Show Source):
x hours at 40km/h, plus y hours at 30km/h, equals 470km:
ANSWER: 8 hours at 40km/h and 13-8=5 hours at 30km/h
CHECK: 40(8)+30(5) = 320+150 = 470
Here is a very different way of solving this kind of problem. It is essentially a "mixture" problem -- you are mixing two speeds to get an overall average speed in between the two speeds.
The idea is to see how far he would have traveled if all 13 hours had been at either 30km/h or 40km/h, then look to see where the actual distance lies between those two distances.
(1) 13 hours all at 30km/h would make 390km; 13 hours all at 40km/h would make 520km
(2) The actual distance of 470km is 8/13 of the way from 390 to 520. (390 to 520 is 130; 390 to 470 is 80; 80/130 = 8/13)
(3) That means 8/13 of the total time was at 40km/h.
ANSWER: 8/13 of 13 hours is 8 hours; so 8 hours at 40km/h and the other 5 hours at 30km/h.
You may start from this system of 2 equations in 2 unknowns
x + y = 13 (1)
40x + 30y = 470 (2)
From equation (1), express y = 13-x and substitute it to equation (2)
40x + 30*(13-x) = 470. (3)
It gives
x = = 8.
ANSWER. x= 8 hours; y = 13-8 = 5 hours.
Another way to solve the problem is to start from equation (3), by considering it as an independent setup.
