Bunuel wrote:
Walking at 3/4 of his normal speed, Mike is 16 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and his office is
A. 42 minutes
B. 48 minutes
C. 60 minutes
D. 62 minutes
E. 66 minutes
Let's start with a
word equationDistance traveled at 3/4 speed =
Distance traveled at regular speedLet
v = regular walking speed (in miles/minute)
So,
3v/4 = REDUCED walking speed (in miles/minute)
Let
t = regular travel time (in minutes)
So,
t + 16 = travel time (in minutes) when walking 3/4 speed
Distance = (speed)(time)So, we get:
(3v/4)(t + 16) =
vtExpand: 3vt/4 + 12v = vt
Multiply both sides by 4 to get: 3vt + 48v = 4vt
Subtract 3vt from both sides: 48v = vt
Rewrite as: vt - 48v = 0
Factor: v(t - 48) = 0
So, EITHER v = 0 PR t = 48
Since the speed (v) cannot be zero, it must be the case that t = 48
Answer: B
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