SOLUTION: The average speed of a car over a certain distance is calculated by dividing the total distance travelled by the total time taken. Two towns A and B are 10km apart, a motorist trav

Question 1201574: The average speed of a car over a certain distance is calculated by dividing the total distance travelled by the total time taken. Two towns A and B are 10km apart, a motorist travels from A to B at an average speed of 20km per hour and travels from B to A at an average 40km per hour.
(a) Determine the average speed to the motorist for the two trips combined. (I.e. from A to B and back to B and back to A)
(b) Determine the speed would the motorist have to average on the return trip from B to A to yield an overall speed of 30km per hour? Assume the motorist has averaged 20km per hour from A to B

Found 2 solutions by mananth, Theo:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

a motorist travels from A to B at an average speed of 20km per hour
distance =10km
time = 10/20 = 0.5 hours

and travels from B to A at an average 40km per hour.
10/40 = 0.25 hours
Total time = 0.75 hours
Total distance = 20 km
Speed = D/T = 20/0.75 = 26.67 km/h
30 = 20/ total time
Let return time be x
30 = 20/(0.5+x)
30(0.5+x) = 20
15+30x = 20
30x =5
x= 5/30 = 1/6 hour
Time B to A is 1/6
Distance /time = speed
10/ (1/6) =60 km/h should be the return speed to get average of total travel

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A to B = 20 km per hour.
B to A = 40 km per hour.
D from A to B and from B to A is equal to 10.
rate * time = distance.
let x = the time it takes to get from A to B.
let y = the time it takes to get from B to A.
you get:
20x = 10
40y = 10
solve for x to get x = 1/2 hour.
solve for y to get y = 1/4 hour.
total time to get from A to B and from B to A is 1/2 + 1/4 = 3/4 of an hour.
rate * time = distance becomes rate * 3/4 = 20
solve for rate to get rate = 20 / (3/4) = 80/3 kmph.
average speed is 80/3 kmph = 26 and 2/3 kilometers per hour.
if you want the aveage speed to get from A to B and then from B to A, to be 30 kmph, then rate * time = distance becomes 30 * time = 20.
solve for time to get time = 2/3 of an hour.
since going from A to B still takes 1/2 hour, then you get:
1/2 + y = 2/3 of an hour.
solve for y to get:
y = 2/3 - 1/2 = 4/6 - 3/6 = 1/6.
going from A to be takes 1/2 hour and going from B to A would have to take 1/6 of an hour.
since B to A is 10 km, you get rate * 1/6 = 10 which gets you rate = 60 kmph.
to have the overall speed equal 30 kmph, A to B would be at 20 kmph and B to A would be at 60 kmph.
20x = 10 becomes x = 1/2
60y = 10 becomes y = 1/6
1/2 + 1/6 = total time of 4/6 of an hour.
rate * time = 20 becomes rate * 4/6 = 20
solve for rate to get rate = 20/(4/6) = 20*6/4 = 30 kmph.
average speed round trip is 30 kmph.
answer to a is 80/3 kmph average for the round trip = 26 and 2/3 kmph.
answer to b is average speed from B to A would have to be 60 kmph so that the overall round trip average is 30 kmph.

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