# math

posted by annika

two joggers used a 2 km circular road for their training. if they start together from the same place and jog in opposite directions, they meet after 15 minutes. However, if they jog in the same direction at the end of one hour and 15 minutes, the faster jogger would have gone 1 1/4 laps farther. How fast did each jog?

1. Reiny

rate of faster --- x km/h
rate of slower --- y km/h

going in opposite direction:
distance covered by slower = (1/4)y
distance covered by faster = (1/4)x

(1/4)x + (1/4)y = 2
x + y = 8

going in same direction:
distance covered by faster = (5/4)x + 1/2 , (1/4 lap is 1/2 km)
distance covered by slower = (5/4)y

(5/4)x + 1/2 = (5/4)y
5x + 2 = 5y
5x - 5y = -2

multiply the first by 5
5x+5y = 40
5x - 5y = -2
10x = 38
x = 3.8
then y = 4.2

check:
opposite directions:
the faster went (1/4)(4.2) = 1.05 km
the slower went (1/4)(3.8) = .95
which adds up to 2 km, or 1 lap

same direction:
faster went (5/4)(4.2) = 5.25
slower went (5/4)(3.8) = 4.75
5.25 - 4.75 = .5 km, or 1/4 of a lap

all is good

## Similar Questions

1. ### Physics

Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 1.2 10-3 rad/s, while the other has an angular speed of 3.4 10-3 rad/s. How long will it be before they meet?
2. ### math

two joggers start at the same time from opposite ends of a 10-km course. One jogger is running at 6 km/h and the other is running at 10 km/h. How long after they begin will they meet?
3. ### Algebra

Starting at the same point, Angie and Payton jog in opposite directions. Angie can jog 1.5 miles per hour faster than Payton. After 2.5 hours, they are 20 miles apart. How fast can each person jog?
4. ### Algebra

Starting at the same point, Angie and Payton jog in opposite directions. Angie can jog 1.5 miles per hour faster than Payton. After 2.5 hours, they are 20 miles apart. How fast can each person jog?
5. ### Physics

Two friends are at the local high school track, a circle measuring 440 yards for one complete lap. Abe can jog at 8.2 miles per hour while Bobâ€™s jogging speed is 4.6 miles per hour. If they both start at the same point and jog in …
6. ### Math

you've been to jog for 1 hr a day 3 times a wk, if you jog 5.5 miles per hr, how far will you jog each wk
7. ### Math

Two bike riders ride around a circular track, 1st rider completes one round in 12 minutes, the second rider completes a round in 16 minutes. If they start at the same time and fo in the same direction, how many turn before they meet …
8. ### physics

Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 2.46 x 10-3 rad/s, while the other has an angular speed of 7.91 x 10-3 rad/s. How long will it be before they meet?
9. ### intermediate math

angie and payton jog of opposite each other and angie can jog 4.5 mile faster than payton. after 1.5 hours they are 17 miles apart. how much can each person jog
10. ### math

Danny and Erica are 3km apart on a straight road. They set out to walk uniformly at the same time. If they walk in an opposite direction, they will meet after 24 minutes. If they walk in the same direction, Danny will catch up to Erica …

More Similar Questions