A person can walk at a constant rate of 8mph and can bike at a rate of

Question

A person can walk at a constant rate of 8mph and can bike at a rate of 16mph. If he wants to travel 80 miles in 8 hours using bike and walking at their constant rates, how much distance would he require to walk?

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

A. 20
B. 30
C. 48
D. 60
E. 72

OA after three days

chetan2u · Accepted Answer

Hi Vyshak,
you are correct, BUT   Alligation or Weighted average method.. is the fastest method in such Qs
 It enables us to find the ratio in which two or more ingredients at the given price/%/weight must be mixed to produce a mixture of a desired price/%/weight.

Lets manipulate this Q to fit into weighted average method--

here the walking speed= 8mph, so time he would take cover 80miles= 80/8=10 hr
similarly the biking speed= 16mph, so time he would take cover 80miles= 80/16=5 hr

But the average has to be 8hrs, so the ratio of dist by walking =  \frac{(Avg-biking time)}{(walking time-biking time)}= \frac{(8-5)}{(10-5)}= \frac{3}{5} 
so the distance travelled = 3/5 th of total = 3/5 *80 = 48

Kurtosis · Answer

Total distance = 80
Distance = Speed * Time
Walking speed = s1 = 8
Walking time = t1 
Bike speed = s2 = 16
Time traveled in bike = t2

d1 + d2 = 80
s1t1 + s2t2 = 80
8*t1 + 16*t2 = 80
t1 + 2*t2 = 10 ----- (1)
Given: t1 + t2 = 8 ----- (2)

(1) - (2) --> t2 = 2 and t1 = 8 - 2 = 6

Walking distance = s1*t1 = 8*6 = 48

Answer: C

powellmittra · Answer

Hi Chetan2u, Please add OA to the question. Thanks!

Divyadisha · Answer

I backsolved this question

Total distance= 80 miles Total time= 8 hrs First check for option 'C' 48 miles of walking means he walked for 48/8= 6 hrs Remaining 32 miles of biking means he biked for 32/16= 2 hrs Total hours traveled= 6+2 = 8hrs (as mentioned in the question stem)

Abhishek009 · Answer

AN ALTERNATE APPROACH Check the answer options , the correct answer for walking must be a multiple of 8 and for bike must be multiple of 16 , so possible answers are C. 48 & E. 72 Back solve C. 48 Walk = 48 miles ; Bike = 32 Walking speed = 8 miles/hr ; Biking speed = 16 miles/hr Walking time = 6 hr ; Biking speed = 2 hr ( total time is 8 hours ) E. 72 Walk = 72 miles ; Bike = 8 Walking speed = 8 miles/hr ; Biking speed = 16 miles/hr Walking time = 9 hr ; Biking speed = 1/2 hr ( total time is 19/2 hours ) Hence correct answer must be (C) :-D

Ferrarif1286 · Answer

time of bike: b
time of walk: w
b+w=8 -> b=8-w

D=Rt:
8w+16b =80
substitute b: 8w+16(8-w)=80. Solving for w and get w=6.
To get the total distance of walk, multiply 6 by 8 = 48. C

gauravk · Answer

chetan2u

Thanks for the solution, I was able to solve it using traditional method and was able to follow your weighted average method.

Can you pls explain that instead of using Average time taken for weighted average method, why can't we use directly the respective speeds given ( 8 mph, 16 mph etc).

TIA

KarishmaB · Answer

gauravk

SpeedW - 8 mph
SpeedB - 16 mph

Avg speed = 80/8 = 10 mph

TW/TB = (SpeedB - SpeedAvg)/(SpeedAvg - SpeedW) = (16 - 10)/(10 - 8) = 3/1

So he walked for 3/4th of the time i.e. for (3/4)*8 hrs = 6 hrs. (Note that when averaging speed, the weights will always be time taken, never distance.)
In 6 hrs, he would have walked a distance of 8*6 = 48 miles

Answer (C)

gauravk · Answer

VeritasPrepKarishma

Thanks a lot for the explanation, I was going wrong with the highlighted part. I was using the ratio directly on the total distance (which obviously wasn't working).

Is there a mathematical derivation of the highlighted part which can help me understand this, rather than cramming it.

TIA.

KarishmaB · Answer

Check here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/1 ... -averages/

rohit8865 · Answer

similar approach by  Vyshak  and  chetan2u  but in different pattern

let distance covered by walking =W & by bike=B
As avg speed on travelling both by walking and bike=80km in 8 hrs==10km/hr

we can arrange in avg. speed formula=total distance /total time
(W+B)/{W/8+B/16}=10
(16W+16B)/(2W+B)=10
16W+16B=20W+10B
B=2/3W--------------(I)
as total distance W+B=80
putting value of B from (I)
W+2/3W=80
W=48

Ans C

Sirakri · Answer

W=Time spent walking
B=Time spent biking

80=16B+8W
=>W=10-2B
But, W+B=8 (given)
=>W=10-2(8-W)
=>W=6

=> Distance walked=6*8=48miles

C

rickyreign · Answer

Distance = Speed * Time
Let speed and time for walking be s1 and t1 respectively
Let speed and time for biking be s2 and t2 respectively
t1+t2=8
t2=8-t1
(s1*t1)+(s2*t2)=80
Substituting values
(8*t1)+(16{8-t1})=80
t1=6
Distance travelled by walking = 8*6= 48 i.e C

LetsDoIt2022 · Answer

8\frac{m}{h}*(8h-x) + 16\frac{m}{h}*x = 80m 
 8\frac{m}{h}*x = 16m 
 x = 2h

Distance walked on foot:  8\frac{m}{h}*(8h-2h) = 48m

bumpbot · Answer

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A person can walk at a constant rate of 8mph and can bike at a rate of

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