Question

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?

Answer 1

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