OG 132

[stmifx]

How long did it take Betty to drive nonstop to a trip from here home to Denver.

1) If Betty's avg. speed for the trip had been 1 1/2 OR 3/2 times as fast , the trip would have taken 2hours.

2) Betty's avg. speed for the trip was 50 mph

 

How does the [tooltip=Official Guide]OG[/tooltip] conclude that if Betty drove 3/2 times fast then it will take her 2/3 as much time.?

 

Thanks in advance.

 

 

 

[GMAT-HELP]

Let Original speed = R; Time = T hrs

R*T = D -----(1)

If 3/2 times fast, T= 2 hrs =>

(3/2) * R *2 = D -----(2)

which gives D = 3R

Substituting D = 3R in eqn (1), we get

R*T = 3R

T = 3 hrs.

 

Hope this helps.

 

Thanks,

GMAT-HELP

[ursula]

Remember that distance = speed * time.

If we multiply Betty's speed by 1.5, we need to divide her time by 1.5 so that she ends up covering the same total distance.

distance = speed*1.5 * time/1.5

 

Or, using fractions:

distance = speed*3/2 * time/(3/2)

= speed*3/2 * time*2/3

 

If this is confusing, look at a simpler case: If her speed had been twice as fast (multiply by 2), the time taken would have been half as long (divide by 2).

 

Of course this is data sufficiency, so you don't actually need to calculate the numerical answer.