How to solve this math problem?

Question

Two cyclists start biking from a trail's start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?

Answer 1

7 hours and 48 minutes

Sameera joshi,

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Answer 2

It will take 4.5hr (270 min) for the 2nd cyclist to to catch 1st cyclist

soln:

1st cyclist 3 hr before 2nd cyclist i.e, x+3

so for 1st cyclist 6* (3 + x)

for 2nd cyclist 10 * x

1st cyc = 2nd cyc

(3+x)* 6 = x* 10

18 + 6x = 10x

x = 18/4

x = 4.5 hr

hope this is enough to understand

so for 1st cyclist (3+4.5)*6 = 45 mile

    for 2nd cyclist 4.5 * 10 = 45 mile

so both will meet at the 45th mile

Answer 3

The answer is 4 1/2 hours.

When the second cyclist starts, the first cyclist has already traveled 18 miles.  In the following equation, x represents the number of hours both cyclists traveled at their respective speeds to reach the same location.

18 + 6x = 10x

18 = 4x

x = 4.5