Smriti Shashikumar wrote: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
