Word problem?

Question

Marlene rides her bike to her friend Jon's house and returns home by the same route. Marlne rides her bike at constant speeds of 6 mph when going uphill and 12 mph when going downhill. If her total time riding was 2 hours, how far is it to Jon's house?

Any help would be appreciated!

Answer 1

The equation would be:

(x/6) + (x/12) = 2
(2x/12) + (x/12) = 2
(3x/12) = 2
x/4 = 2
x = 8 miles

Answer 2

Since her speed uphill is 6 mph and her downhill speed is 12 mph, in 2 hours she would have covered 6 + 12 = 18 miles and thus the distance to Jon's house is 18/2 = 9 miles one way.

Answer 3

Let a be length of route going uphill, and
b be length of route going downhill.
So, a/6 + b/12 + a/12 + b/6 = 2.
Or, 3a/12 + 3b/12 = 2.
Or, multiplying each side by 4, a+b=8.

SO, its 8 miles to jon's house.

Answer 4

The key to this problem is that the 6 and 12 cancel each other out, and the average speed is 9 miles per hour over the whole course (her house is at the same altitude when she leaves and when she gets back.) Distance to Jon's house is 9 miles.

Ron.

Answer 5

Try this. x = total distance uphill or downhill so:
x = 6 mph * t1 uphill and
x = 12 mph * t2 downhill then
t1 + t2 = 2 hr. so t1 = 2 hr - t2
then 6 mph * t1 = 12 mph *( 2 hr - t1) solve for t1 after that you can calculate de distance.
Hope it is useful for you.

Answer 6

The time it takes to go to Jon's house:
T1 = Du/Vu + Dd/Vd where Du is the distance traveled uphill to Jon's house and Vu her speed when going uphill (6mph), Dd is the distance traveled downhill, and Vd the downhill speed (12mph)
On Her way back, Du and Dd are obviously inverted (if she was going uphill on her way there, she is going downhill on her way back)
so T2 = Du/Vd + Dd/Vu
T1+T2 = 2 hours = (Du+Dd)/Vu + (Du+Dd)/Vd
Du+Dd is the total distance to Jon's house, Du+Dd=D
D = (T1+T2)(VuVd)/(Vu+Vd) = 2*6*12/18= 8miles.

Answer 7

9 miles.
i think