Tim and Élan are 90 miles away from one another. They are starting to

Question

Tim and Élan are 90 miles away from one another. They are starting to move towards each other simultaneously, Tim at a speed of 10 Mph and Élan at a speed of 5 Mph. If every hour they double their speeds, what is the distance that Tim will pass until he meets Élan?

(A) 30 miles.
(B) 35 miles.
(C) 45 miles.
(D) 60 miles.
(E) 65 miles.

(A) 30 miles. 
(B) 35 miles. 
(C) 45 miles. 
(D) 60 miles. 
(E) 65 miles.

KarishmaB · Accepted Answer

The ratio of speeds of Tim and Elan is 2:1. When their speed doubles, the ratio still remains 2:1 since the speed of both doubles. 
So, in the same time, whatever distance is between them, they will cover it in the ratio 2:1.
Since distance between them is 90 miles, which is equivalent to 3 on the ratio scale, it gives us the multiplier 30.
The actual distance covered by Tim is 2*30 = 60 miles.

Answer (D)

sudhirmadaan · Answer

D is the answer
total distance between them is 90 
first hour 
5+10 = 15 distance is covered 
second hour 
10+20= 30 distance is covered 
third hour 
20+40= 60 but remaining is 45 to be covered so calculate time here 
60 miles in 1 hour 
45 miles in -- 45/60 = 3/4 hour 
T speed is 40 this time so ... distance covered by him is 3/4*40 = 30
total dis by T is 10+20+30= 60

adiagr · Answer

In 1st hour: Relative speed of the two will be 10+5 = 15 miles / hour. As they move towards each other, The distance between them reduces by 15 miles. Distance left between them: 90 - 15 = 75 miles.

In 2nd hour: Speed of Tim: 20Mph, That of Elan: 10 Mph. Relative speed of the two will be 20+ 10 = 30 miles / hour. As they move towards each other, The distance between them reduces by 30 miles. Distance left between them: 75 - 30 = 45 miles.

In 3rd hour: Speed of Tim: 40 Mph, That of Elan: 20 Mph. Relative speed of the two will be 40+ 20 = 60 miles / hour.

Now in order to cover the remaining distance of 45 miles. They will take: (45/ 60) hrs. = (3/4) hour.

Distance travelled by Tim?

In first hour: 1 hour * (10 miles per hour) = 10 miles
In second hour: 1 hour * (20 miles per hour) = 20 miles
In third hour: (3/4) hour * (40 miles per hour) = 30 miles

Total distance travelled: 10+20+30 = 60 miles.

D is the answer.

CounterSniper · Answer

Since they are travelling towards each other the speed needs to abe added !!

Distance = 90 miles
first hour !!
 total distance travelled = 10+5=15 miles
 distance left = 90-15 =75 miles
second hour !!
 total distance travelled = 20+10=30 miles (speed doubles)
 distance left = 75-30=45 miles
third hour !!
 total distance travelled = 40+20=60 miles 
 since distance left is only 45 miles 
 time taken to complete 45 miles = 45/60 = 3/4 hour 
 in this period , distance travelled by tim = (3/4)*40=30 miles
Total distance travelled by tim = 10 + 20 + 30 = 60 miles

AbdurRakib · Answer

Tim and Elan will meet at the same time while their ratio of speed is 2:1 respectively.So their individual distance traveled ratio will be same.

Plugging in the answer choice Only Answer Choice D meet the 2:1(Tim:Elan=60:30) ratio of maintaining total distance traveled 90 miles

So  Correct answer D

Madhavi1990 · Answer

I solved it with this logic. A little visually though:
------>Tim: 10,20,40,80,160 (we consider only upto 80 as beyond that no point doubling speed)
 80,40,20 ,10,5 <-------
we see the overlap in terms of 40 mph and 20 mph
20 we can discard Elan would be too far even if he doubled his speed, 80 would mean Tim overshot Elan
with regard to 40, we do 90/40 --> 9/4. If we divide 90 into 4 parts we get approx 25/25/25/25 (les than 100 though). 9/4 ~ 3/2 which is then 3 parts out 2; approximately 60 (it has to be more than 45 but less than 65)

Tango3 · Answer

Tim's disatnce after 3.5 hrs is 60 miles
Elan's distance after 3.5 hrs is 30 miles.

Answer D

karnavora1 · Answer

While the ratio method works absolutely fine there are times when one can't think of such elegant answers.

The easier way to do it is a make a table

Distance Tim Elan
1st Hour 10 5
2nd Hour 20 10
3rd Hour 40 20
3 1/2 Hours 60 30

Hence at 3 1/2 hours Tim meets Elan and has covered 60 Miles.
Answer D

If this answer helped you a kudos is appreciated.

adewale223 · Answer

After 2 hours Tim covers 30 miles and Elan covers 15 miles.

Since ratio of their speeds is 2:1

30 + 2x + 15 + x = 90

3x = 45

x = 15

Therefore distance Tim covers =

30 + 2(15) = 60 miles.

Posted from my mobile device

bumpbot · Answer

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