GRE Reasoning problem time/distance/average speed

Question

David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A) 48

B) $\dfrac{256}{5}$

C) $\dfrac{360}{7}$

D) $\dfrac{105}{2}$

E) $\dfrac{160}{3}$

Solution: (C)

My answer:

$\begin{align} t_1 &=\dfrac{v_1}{d} = \dfrac{45}{d} \\ t_2 &=\dfrac{v_2}{d} = \dfrac{60}{d} \end{align}$

and

$t = t_1 + t_2 =2$

so: $\hspace{5mm} d =\dfrac{105}{2} \hspace{5mm}$ (D)

Apparently, my thinking is wrong, but I don't know where.

Any thoughts? Very much appreciated!

Think about units. If you divide speed by distance, you have (miles/hr)/miles, so you do not get time. Remember that distance is speed $\times$ time (assuming constant speed). — Ted Shifrin, Mar 03 '17 at 22:22

score 0 · Accepted Answer · edited Mar 03 '18 at 18:22

0

Your formula is slightly off- you should have $v_1\cdot t_1=d$ and $v_2\cdot t_2=d$. You can see this with units of measurement: miles per hour can be expressed as $\frac{\text{miles}}{\text{hours}}$ and time as $hours$ so there product should be distance as $miles$. If you want to verify, your answer should be $C$.

edited Mar 03 '18 at 18:22

Siong Thye Goh

149,520
20
88
149

answered Mar 03 '17 at 22:23

Kevin Long

5,159

Yes of course, thank you for the prompt reply! I messed up here! – QFi Mar 03 '17 at 22:27

score 0 · Answer 2 · answered Mar 03 '17 at 22:33

Another way to solve this is by harmonic mean. Since you are given two average speeds over same distance, average speed of total travel is given by $$v = \frac{2}{\frac 1{v_1} + \frac 1{v_2}} = \frac{2}{\frac 1{45} + \frac 1{60}} = \frac{360}{7}\,\text{mph}$$

Since twice the distance from home to work takes $2$ hours at that speed, the distance is precisely $\frac{360}7$ miles.

score 0 · Answer 3 · answered Mar 03 '18 at 18:03

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A simple way would be just to say

$t_{total} = t_{home}+t_{work} = \frac{d_{home}}{v_{home}} +{\frac{d_{work}}{v_{work}}}$

We know that $$d_{home}=d_{work}$$

So just plug in the values and solve for d

answered Mar 03 '18 at 18:03

dman

1

score 0 · Answer 4 · edited Dec 12 '18 at 17:48

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since the rate from home to work and from work to home has been given which are $45\mathrm{mph}$ and $60\mathrm{mph}$ respectively. Let x represent distance: then $$ time = distance /rate $$ from home to work, $t= x/45$,
while from work to home $t = x/60$, where total time $= 2$ hours, therefore $$ \begin{split} x/45 + x/60 &= 2\text{ hours} \\ 60x +45x /2700 &= 2\\ 5400/105 &= 51.428... \end{split} $$

hence from the answer options $= 360/7$.

edited Dec 12 '18 at 17:48

Daniele Tampieri

9,727

answered Dec 12 '18 at 17:16

Noah Darko-Adjei

1

Welcome to MSE. Your answer adds nothing new to the already existing answers. – José Carlos Santos Dec 12 '18 at 17:36

score 0 · Answer 5 · answered Aug 29 '19 at 08:14

0

S1=D/t1 45=D/t1 S2=D/t2 60=D/t2 t1+t2=2 Average speed=Total distance/total time taken total time=total distance/average speed 2=D/45+D/60 solving D=360/7

answered Aug 29 '19 at 08:14

Gowthami Kuttapalayam Mothilal

1

Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. – José Carlos Santos Aug 29 '19 at 08:29

GRE Reasoning problem time/distance/average speed

5 Answers5