Problem Solving

Jane travel a distance of 60 miles @ 30 mph and another 90 miles @ 60 mph. What is her average speed for the entire journey (in mph)?

A) 40
B) 42.8
C) 45
D) 52.3
E) 54.7

Total distance = 150 miles


distance=60 miles speed=30mph

time =60/30=2

distance=90 miles speed =60mph

time=90/60=1.5

AS=Total distance/Total time=150/(2+1.5)=150/3.5

42.8

Option B

30 Second Hack:

Since Jane spent 2hrs traveling at 30mph, and 1.5hrs traveling at 60mph, her average speed (a weighted average) must be closer to 30mph than to 60mph. 45 is halfway between the two (it's the average), so the answer must be less than 45.

Guess A or B.

40 is the only 'round' answer choice. Not likely to be correct.

Guess B.

2.If object covers part of journey at speed p and remaning at speed q and diatance are in ration m:n

Average speed=(m+n)pq/(mq+np)

m:n=60:90=2:3

p=30 q =60

AS=5*30*60/(129+90)=42.8