Anne and Beth will participate in a sack race (In a sack race, people

Question

Anne and Beth will participate in a sack race (In a sack race, people hop to reach the finish line). In the time that Anne takes 3 hops, Beth takes 4 hops but the distance covered by Anne in 4 hops is equal to distance covered by Beth in 5 hops. What is the ratio of Anne’s speed: Beth’s speed?

A. 3 : 5
B. 12 : 20
C. 15 : 16
D. 1 : 1
E. 5 : 3

A. 3 : 5
B. 12 : 20
C. 15 : 16
D. 1 : 1
E. 5 : 3

Vetrik · Accepted Answer

Let time taken by Anne and beth to complete 3 and 4 hops respectively be 't'

Therefore time taken by Anne & Beth to do 1 hop is 't/3' & 't/4'

Let distance covered in Anne & beth's 4 & 5 hops respectively be 'd'

There distance covered by Anne & beth in 1 hop is 'd/4' & 'd/5'

Anne's speed: Beth's speed =   /   :   /   =  *  :   *   = 15:16

Bunuel · Answer

The distance covered by Anne in 4 hops is equal to distance covered by Beth in 5 hops --> 4*(distance of Ann's 1 hop) = 5*(distance of Beth's 1 hop).

The time that Anne takes 3 hops, Beth takes 4 hops --> time for Ann to take 12 hops --> 3*(time for Ann's 1 hop) = 4*(time for Beth's 1 hop).

Divide one by another:

4/3*(distance of Ann's 1 hop)/(time for Ann's 1 hop) = 5/4*(distance of Beth's 1 hop)/(time for Beth's 1 hop);

4/3*(Anne's speed) = 5/4*(Beth's speed);

4/3*(Anne's speed)/(Beth's speed) = 15/16.

Answer: C.

Thoughtosphere · Answer

Since A & B cover the same distance in 4 and 5 hops respectively, we can say that distance covered in 4 hops by A = distance covered in 5 hops by B = x
Distance covered by A in 1 hop = x / 4
Distance covered by B in 1 hop = x / 5
Now, A and B make hops in the ratio of 3 : 4 for a given time interval.

Thus distance covered by A in 3 hops = 3x/4
Distance covered by B in 4 hops = 4x/5

Since these above mentioned distances are covered in a stipulated time, so their ratios will be equal to the ratios of their speed

Ratio of A's speed to B's Speed = 3x/4 : 4x/5 = 15 / 16

pqhai · Answer

My approach

Distance covered by Anne in 4 hops = distance covered by Beth in 5 hops

Premise #1: Equal distance

Assume Distance = 10  (Plug in always helps)
=>  1 hop  of Anne = 10/4 =  2.5 
=>  1 hop  of Beth = 10/5 =  2

Premise #2: Equal time

Time Anne took  3 hops  = t
=>  V1 = D1/t = (2.5*3)/t

Time Beth took  4 hops  = t
=>  V2 = D2/t = (2*4)/t

=>  V1/V2 = 7.5/8 = 15/16

Ans: C

Divyadisha · Answer

Let the time Anne takes for 3 hops and Beth takes for 4 hops = x

Anne takes x mins for 3 hops, so she will take 4x/3 mins for 4 hops

Beth takes x mins for 4 hops, so she will take 5x/4 mins for 5 hops.

We know distance= Speed *time (distance covered by Anne and Beth is same)

S1T1=S2T2
S1*4x/3= S2*5x/4

S1/S2= 15/16

C is the answer

gracie · Answer

anne's time per hop=4/3 of beth's
anne's distance per hop=5/4 of beth's
anne's speed=(5/4)/(4/3)=15/16 of beth's
ratio of anne's speed to beth's=15:16

CAMANISHPARMAR · Answer

AB1.jpg AB2.jpg Speed = \frac{Distance}{time} Speed of Anne from aforesaid is \frac{20 Miles}{16 minutes} = \frac{5}{4} Similarly Speed of Beth from aforesaid is \frac{20 Miles}{15 minutes} = \frac{4}{3} Ratio of speed of ANNE:BETH = \frac{5}{4} Divided by \frac{4}{3} or \frac{5}{4} * \frac{3}{4} = \frac{15}{16} Therefore correct answer is C

Swat2020 · Answer

Let total Distance = D

So we can assume that Anne is covering the distance D in 4 hops and Beth is covering the same distance in 5 hops

Let time taken by Anne in 3 hops and Beth in 4 hops = T

Time per hop (Anne): T/3
Time per hop (Beth): T/4

Remaining hops to cover by Anne = 4-3 = 1
Remaining hops to cover by Beth = 5-4 = 1

Therefore,
Total time to cover Distance D by Anne = T + T/3 = 4/3T
Total time to cover Distance D by Beth = T + T/4 + 5/4T

Ratio of time (Anne: Beth) = 4/3  /  5/4 = 16:15

Ratio of speed is inversely proportional to Ratio of time

Therefore, ratio of speed =  15/16

matteotchodi · Answer

here is my solution

keep track of UNITS and you will make everything more straightforward!

bumpbot · Answer

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