In a 10 km race. A, B, and C, each running at uniform speed, get the

Question

In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?

A. 1750
B. 1800
C. 1900
D. 1950
E. 2000

nick1816 · Accepted Answer

Speed of A, B, and C are  S_A ,  S_B  and  S_C  respectively.

S_A : S_B = 10:9

S_B : S_C = 10:9

S_A : S_B : S_C = 10*10 : 9*10 : 9*9 = 100 : 90 : 81

A beat C by 1.9 (10-8.1) Km or 1900m.

firas92 · Answer

The distance between B and C increases at the rate 1km for every 10km

So when B runs 9km, the distance between B and C must be 9/10=0.9km=900m

Distance AC = AB+BC = 1000+900 = 1900m

Answer is C

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Shahalikhan · Answer

when a reaches finish line b reaches 9km (i)
 when b reaches finish line c reaches 9km (ii)

from (i) same equating time

S denotes speed

10/S(a)=9/S(b)

=> 10/9S(a) =1/S(b)

similarly from ii

10/s(b) = 9/s(c)

1/s(b)= 9/10s(c)

equating for 1/s(b), we get relation between s(a) and s(c)

10/9S(a) =9/10s(c) => s(c)=81S(a)/100

running at uniform speed c could only cover 81/100 of distance covered by A

so while covering 10000 metres c could only cover 81/100*10000=8100

so answer is c 1900m

sankarsh · Answer

An excellent way to solve it!!!!
Took me close to 4 min by the traditional (R*T=D) method

ScottTargetTestPrep · Answer

Let’s let the time A runs the 10 km (or 10,000-meter) race be 1000 seconds. Thus, A’s speed is 10,000/1000 = 10 m/s. Since B is 1 km behind A when A finishes the race, B runs 9 km, or 9000 meters, in 1000 seconds. Thus, B’s speed is 9000/1000 = 9 m/s. In other words, B runs the 10 km race in 10,000/9 seconds. Since C is 1 km behind B when B finishes the race, C runs 9 km, or 9000 meters, in 10,000/9 seconds. So C’s speed is 9000/(10,000/9) = 9/(10/9) = 81/10 = 8.1 m/s.

Now, let’s compare A and C when A finishes the race. A finishes the 10 km race in 1000 seconds (see above). During this time, C runs 8.1 x 1000 = 8100 meters. Therefore, A beats C by 10,000 - 8100 = 1900 meters.

Answer: C

Kinshook · Answer

Given: In a 10 km race. A, B, and C, each running at uniform speed, get the gold, silver, and bronze medals, respectively. 
Asked: If A beats B by 1 km and B beats C by 1 km, then by how many metres does A beat C?

A beats B by 1 km
A travels 10 kms in the same time, B travels 10-1 = 9 kms
Va / Vb = 10/9

B beats C by 1 km
B travels 10 kms in the same time, C travels 10-1 = 9 kms
Vb / Vc = 10/9

(Va/Vb )*(Vb/Vc) = (10/9)*(10/9) = 100/81
When A travels 10 kms, V travels 8.1 kms

Meter by which A beats C = (10-8.1)*1000 = 1900 meters

IMO C

sarthak1701 · Answer

Let's assume A's speed is 1km/minute

1km * 10 = 10, A finishes the race in 10 mins

At the same time, B has covered 9 km

Therefore B's rate is 9/10

B will finish the race in 9/10*T = 10, T = 100/9 minutes

At the same time, C has covered 9 km

Therefore C's rate = R*100/9 = 9, R = 81/100

When A has finished the race (in 10 minutes)

C has covered = 81/100 * 10 = 8.1 km

So A has beaten C by 1.9 km or 1900 metres. Ans C

In a 10 km race. A, B, and C, each running at uniform speed, get the

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GMAT Problem Solving (PS) Questions

In a 10 km race. A, B, and C, each running at uniform speed, get the

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