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(1) A car traveled from Dar es salaam to morogoror at 120km/h and returned to dar es salaam at 80km/h.
find average speed for the entire journey.(use both kinematic and harmonic mean technique)
(2) tap P can fill a tank in 6 hours and tap Q can fill the same tank in 9 hours.
if the two taps are turned at the same time, how long will the two taps take to fill the tank
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(1) kinematic technique
Let d be one way distance (in kilometers).
Then the entire trip is 2d kilometers.
The time for the first half of the trip is hours.
The time for the second half of the trip (returning back) is hours.
Total time is the sum + .
Average soeed for the entire trip is the total distance 2d divided by the total time
average speed = = canceling d in both numerator and denominator = =
= = = = 12*8 = 96 km/h. ANSWER
harmonic mean technique
Use the harmonic mean formula for the average speed
average speed = = = 96 km/h
which we, actually, derived in the kinematic solution.
This harmonic mean formula is valid for any trip, consisting of two equal parts at given average velocities
and for each part.
(2) tap P fills of the tank volume per hour.
tap Q fills of the tank volume per hour.
Working together, both taps fill + = = = of the tank volume.
Hence, the tank will be filled in = 3 hours = 3 hours and 36 minutes, if both taps work simulaneously.
Solved.