Distance "Word" Problems

[Smriti Shashikumar]

Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

Thanks for the help as always!

[guerrero]

Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

Thanks for the help as always!

your equation would be -

5*(t-24/20)+6*t=20
t=2hrs

t= this is the time when they meet

Therefore,Tom would have traveled - 8 miles . (B) Ans

[GMATGuruNY]

Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

Thanks for the help as always!

Before Tom starts to walk, Cathy travels alone at rate of 6 miles per hour for 2/5 of an hour:
Distance = r*t = 6*(2/5) = 12/5 miles.
Remaining distance = 20 - 12/5 = 88/5 miles.
When people travel toward each other, they WORK TOGETHER to cover the distance between them, so we ADD THEIR RATES.
Combined rate for Cathy and Tom = 6+5 = 11 miles per hour.
Since Tom's rate is 5 miles per hour, Tom will travel 5 of every 11 miles traveled by Cathy and Tom together.
Thus, Tom will travel 5/11 of the remaining distance:
(5/11)(88/5) = 8 miles.

The correct answer is B.

[Brent@GMATPrepNow]

Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

I like to begin most speed/distance/time questions with a word equation.
One possible word equation is:
Cathy's travel time = Tom's travel time + 24 minutes

Another word equation is:
Cathy's distance + Tom's distance = 20 miles

Either of these word equations will yield the correct response. Let's continue with the second one.
Let t = Tom's travel time
So, t + 24 minutes = Cathy's travel time
Since our speeds are in miles per hour, we can also say...
So, t + 24/60 hours = Cathy's travel time

Cathy's distance = (speed)(time)
= (6)(t + 24/60)
= 6t + 12/5

Tom's distance = (speed)(time)
= (5)(t)
= 5t

So, we get: Cathy's distance + Tom's distance = 20 miles
6t + 12/5 + 5t = 20
Simplify: 11t + 12/5 = 20
Multiply both sides by 5: 55t + 12 = 100
Simplify: 55t = 88
Divide both sides by 11: 5t = 8

IMPORTANT: Since we already determined that Tom's distance = 5t, we can now see that this equals 8

Answer: B

Cheers,
Brent

[Brent@GMATPrepNow]

Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?

A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles

In my previous post, I used one of two word equations to answer the question. Let's examine another possible word equation.

Since Cathy traveled 24 minutes longer than Tom did, we can write:
Cathy's travel time = Tom's travel time + 24 minutes

Since 24 minutes = 2/5 hours, we can also write:
Cathy's travel time = Tom's travel time + 2/5 hours

We're trying to find the distance Tom traveled, so:
Let D = Tom's distance traveled.
Since their combined distances is 20 miles, we can say:
20-D = Cathy's distance traveled.

Cathy's travel time = distance/speed
= (20-D)/6

Tom's travel time = distance/speed
= D/5

So...
Cathy's travel time = Tom's travel time + 2/5 hours
(20-D)/6 = D/5 + 2/5
Simplify: (20-D)/6 = (D+2)/5
Cross multiply: 5(20-D) = 6(D+2)
Expand: 100 - 5D = 6D + 12
Rearrange: 88 = 11D
Solve: 8 = D

Since D = Tom's travel distance, the correct answer is B

Cheers,
Brent