SOLUTION: The average speed for the first 36 miles was 12mph. The average speed for the next 45 miles was 15mph. What should be the average speed for the next 54 miles so that the overall

Question 66510This question is from textbook Advanced mathematics
: The average speed for the first 36 miles was 12mph. The average speed for the next 45 miles was 15mph. What should be the average speed for the next 54 miles so that the overall average speed would be 15mph? This question is from textbook Advanced mathematics

Found 2 solutions by checkley71, uma:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
36/12+45/15+54/x=135/15
3+3+54/x=135/15
54/x=9-3-3
54/x=3
3x=54
x=54/3
x=18 mph for the 54 mile trip.
Answer by uma(370) (Show Source): You can put this solution on YOUR website!
The average speded for 36 miles = 12mph
Time taken = distance/time
= 36/12
= 3 hrs
The average speed for next 45 miles = 15 mph
Time taken = distance/time
= 45/15
= 3 hrs
Let the speed for the next 54 miles = x mph
time taken = distance/speed
= 54/x
Total distance = 36 + 45 + 54
= 135 miles
Total time = 3 + 3 + 54/x
= 6 + 54/x
= (6x + 54)/x hrs [taking LCM and adding]
THus the average speed for the entire journey = distance /time
= 135/ (6x+54)/x
= 135x/(6x+54)
Given the overall speed = 15 mph
==> 135x/(6x+54) = 15
==> 135x = 15(6x+54)
==> 135x = 90x + 810
==> 135x - 90x = 810
==> 45x = 810
==> x = 810/45
==> x = 18
Thus the speed for the last 54 miles has to be 18 mph to get an overall average speed of 15 mph

Good Luck!!!
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