If a man cycles at 10 km/hr, then he arrives at a certain place at 1

Question

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

(A) 11 km/hr 
(B) 12 km/hr 
(C) 13 km/hr 
(D) 14 km/hr
(E) 14 km/hr

BhishmaNaidu99 · Accepted Answer

As the distances is covered is equal in two cases , let it be x hrs when he travels at 10kmph

d1 = d 2

10 * x = 15 * (x-2) since its 2hrs less when traveled at 15kmph

x = 6hrs , D = 10 * 6 = 60 km

Time take to reach at noon is , x -1 = 5 hrs , speed = 60 / 5 = 12kmph

abhishekdadarwal2009 · Answer

IMO B

From the above we can formulate teh equation as below:

D/10=(D/15)+2
D/10=(D+30)/15

D/2=(D+30)/3

3D=2D+60
So we get D
D=60

Now to get there at 12 or (D/15)+1 we use the below

60/x= (60/15)+1

60/x=5, x=60/5=12

So 12 is the correct answer.

rkoberoi · Answer

Let time taken at 10km/hr is t hr (1 pm)
distance d = 10t ....eq 1

Time taken to reach the same place at 15km/hr will be t-2 hr (11 pm)
distance d = 15 (t-2).....eq 2

As distance is same in both cases equate two equations

10t=15(t-2)
10t=15t-30
time t=6

Speed must he cycle to get there at noon
time = 5 hours (noon)
distance = 60 km (put the value of t in any equation to get distance)
speed = 60/5
12km/hr

gracie · Answer

let t=slowest cyclist's time
because distances are equal, 10t=15(t-2)→
t=6 hrs
distance=60 km
middle cyclist's time=6-1=5 hrs
middle cyclist's speed=60km/5hrs=12 km/hr
B

ScottTargetTestPrep · Answer

Solution:

We can let t = the number of hours it takes to arrive at noon. We can create the equation:

10(t + 1) = 15(t - 1)

10t + 10 = 15t - 15

25 = 5t

5 = t

Thus, the distance is 10(5 + 1) = 60. To arrive in 5 hours, he must cycle at a rate of 60/5 = 12 km/hr.

Alternate Solution:

Let the distance be d. If he cycles at 15 km/h, he will arrive 2 hours earlier than if he cycled at 10 km/h; thus we have:

d/10 - d/15 = 2

Multiply each side by 30:

3d - 2d = 60

d = 60 km

If he cycles at 10 km/h, it takes the man 60/10 = 6 hours to arrive and we know that it is 1:00 pm when he arrives. If he is to arrive at noon, which is one hour earlier, then it must take him 5 hours and thus, he needs to cycle at 60/5 = 12 km/h.

Answer: B

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If a man cycles at 10 km/hr, then he arrives at a certain place at 1

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