SOLUTION: John drives from point A to point B at a constant speed. On his way back, he drives 20% faster and spends 12 minutes less. How much time does he spend on the round trip?

Question 357003: John drives from point A to point B at a constant speed. On his way back, he drives 20% faster and spends 12 minutes less. How much time does he spend on the round trip?
Found 3 solutions by mananth, robertb, onlinepsa:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
let the speed while going from A to B be s mph
speed from B to A will be 1.2s ( 20% more)
..
D= speed * time
Let time taken from A to B be t hours
time taken from B to A = t-1/5 hours ( 12 minutes = 1/5 hours)
D= st = 1.2s(t-1/5)
st=1.2st -1.2s/5
st-1.2st = -1.2s/5
-0.2st = -1.2s/5
5*-0.2st = -1.2s
-0.1st = -1.2s
divide by s
-0.1t=-1.2
t=1.2
From A t B ity takes 1.2 hours
From B to A it takes 1 hour
So total time for the trip = 2.2 hours
...
m.ananth@hotmail.ca
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
Let x = his speed from A to B. Then 1.20x = his speed from B to A. If t = his time from A to B, then t - 12 is his time from B to A. Using the formula D = RT,
then, we get . We can cancel x from both sides because it is non-zero. hence .
,
. So it took him 72 minutes from A to B. It took him 72-12 minute from B to A. Total travel time is then 72 + 60 = 132 minutes, or 2 hrs and 12 minutes.
Answer by onlinepsa(22)   (Show Source): You can put this solution on YOUR website!
Let, John's usual speed = 's' units/min and the distance between A & B = 'd'
d= s*t, where 't' is the usual time taken to travel AB. ------(Y)
In second case,
d= (s+ 20% of s)(t-12)
=> d= 1.2s (t-12) -----(Z)
(Z) divided by (Y),
1= 1.2(t-12)/t
=>t= 1.2t - 14.4
=>0.2t=14.4
=>t= 72

From, A to B, he takes 72 minutes; thus from B to A he takes 72-12 or 60 minutes. Total time spent on round trip= 60+72=132 minutes.
Faster method:
While the above method involves some equations and steps; the below is a much faster method that involves only mental calculation. Let me explain it in detail so that we nail the point:
S*T = D [In the form of product of two variable such that R.H.S or result is a constant].
S increases by 20%. The equivalent ratio of 20% =1/5. Speed increases by 1/5. Thus, speed becomes 6/5 of the original values. Time will become 5/6 of the original value (to make sure 5,6 get cancelled to render the same result 'D').

Time becomes 5/6th of the original time; time decreases by (1-5/6) or 1/6. This 1/6 is given as 12 minutes. Now, the question is 1/6th of 'WHAT' is 12 minutes. 'WHAT' = 6*12=72 minutes.

Thus usual time =72 minutes (A to B), From B to A, the time will be 60 minutes. Total time =132 minutes.
The above method does not involve any equation and only mental calculation.
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