1.) Peggy walks at a rate of 2 miles per hour and jogs at a rate of 4 miles per hour. She walked and jogged 3.4 miles in 1.2 hours. For how long did Peggy jog and for how long did she walked?

2.) A pilot flew his plane 2400 miles in 8 hours flying with the wind. Flying against the wind over the same route, he returned in 10 hours. What was the rate of the plane and of the wind?

1.

time she spent walking = T

time she spent jogging = 1.2 - T

2T + 4 (1.2 - T) = 3.4

2T + 4.8 - 4T = 3.4

2T - 4T = 3.4 - 4.8

- 2T = - 1.4

T = - 1.4-2 = 0.7 hours = 42 minutes

Time she spent jogging = 1.2-0.7 = 0.5 hours = 30 minutes

2.

Against wind : 2400 miles in 10 hours

With wind : 2400 miles in 8 hours

Speed of plane = x

Speed of wind = y

t=d/r

against the wind speed x-y mph

with the wind x=y mph

2400 / (x-y) = 10

2400 = 10x-10y

240 = x-y eq. 1

2400/x+y=8

2400 = 8x+8y

300 = x+y eq 2

Add eq1 & eq 2 = 740 = 2x

X = 740/2 = 370 mph for plane

300 = 370 + y

Y = 370-300 = 70 mph wind speed

She spent 42 minutes walking and 30 minutes jogging