# Can You Solve This Problem?

suppose jay has travlled x miles,ben has travelled 8-x miles and they meet after time t

for jay: d=x mile, t=t hour and r=5mph
therefore x=5 t
or t=x/5 ...(1)

for ben: d=(8-x) mile, t=t hour and r=7mph
therefore 8-x=7 t
or t=(8-x)/5 ...(2)
from eqns.1 and 2
we have
x/5 = (8-x)/7
or 7x = 40-5x
or x = 40/12 = 3.333 miles
so jay travels 3.333 miles
and ben travels =8-3.333=4.67miles,so ben travels longer distance
combined distance travelled is 8 miles
time at which they meet = 3.333/5=.6666 hrs or 66.66 mins
thanked the writer.
Leo Cillo commented
Let x be Jay's distance and y be Ben's distance.
x + y = 8 mile -- (1)
Since they meet, it took same time:
t = d/r = x/5 = y/7 => 7x = 5y --- (2)
Solving two simultaneous equations (1) and (2) gives:
7x = 5(8-x) => 7x = 40 - 5x => 12x = 40 => x = 3.33333... = 3 1/3
∴ y = 4.66666... = 4 2/3
t = x/5 = (3 1/3)/5 = (10/3)/5 = 2/3 (hr) = 40 (min)
thanked the writer.
It's been awhile; but, let me try: After 40"(40/60)x, Jay traveled 3 1/3 mi. and Ben traveled 4 2/3 miles. The total distance is 8 and the time is 40 minutes.
Check: d=rt 3 1/3mi=5mph(40"=2/3hr)
4 2/3mi=7mph(40"=2/3hr)
thanked the writer.
That can't be right though considering that in one hour, they each would individually have traveled 7 and 5 miles (Their MPH rate) and would have traveled a total distance of 12 miles, not 8. It has to be lower than an hour for them to meet within those 8 miles.
thanked the writer.
Jay and Ben will meet 40 minutes after they start running. Ben will have ran the longer distance, 4.67 miles, rounded to the nearest hundredth. Combined, they will have traveled 8 miles.
thanked the writer.
Gauravsin is correct

Given the equation

8 - t * (5 + 7) = 0 we can simplify it as

t * (5 + 7) = 8

t = 8/(5 + 7) =0.666666666666667

So, the answer is: 0.666666666666667 hours.
thanked the writer. 