Pre Algebra word problem

Question

Ben decides to bike to his friend Matthew’s house to spend the day with him. Matthew, not knowing Ben is on his way over, decides to walk to Ben’s house so they can hang out. Their two houses are 2 miles apart. Ben bikes at a rate of 1/10 of a miles per minute while Matthew walks at a rate of 1/40 miles per hour. At this rate, how long will it take for the two friends to run into each other?

Answer 1

First you must convert the rates to the same units. I choose to convert Ben's rate to mph.

(1/10) miles per minute = 6 mph

Both boys will ravel for the same amount of time, T and they will travel 2 miles in total

6T + (1/40)T = 2 => 241T = 80

and T = 80/241 hrs...a little less than 20 minutes!

Answer 2

rate x time = distance

time = distance/rate

The times are equal.

distance/rate = distance/rate

distance = b + m = 2 b = 2 - m

rate B = 1/10

rate M = 1/40

2 - m/(1/10) = m/(1/40)

(2-m)(10/1) = (m/1)(40/1)

20 - 10m = 40m

20 = 50m

m = 2/5 of a mile

b = 8/5 of a mile

Check:

2/5(40 min/1 mile) = 16 minutes

8/5(10 min/1 mile) = 16 minutes

Answer 3

16 min

X + 4X= 2.0

solve for X