Posted by **Anonymous** on Monday, April 18, 2011 at 3:02pm.

The tour de France is a bicycle race that begins in Ireland but is primarily a race through France. On each day, racers cover a certain distance depending on the steepness of the terrain. Suppose that one particulAr day the racers must comp,tee 210 mi. One cyclist traveling 10 mph faster than the second cyclist, covers this distance in 2.4 h less time than the second cyclist. Find the rate of the first cyclist.

- Algebra -
**Henry**, Wednesday, April 20, 2011 at 5:26pm
Rate of 2nd cyclist = X mi/h.

Rate of 1st cyclist = (x+10) mi/h.

Eq1: d2 = Xt = 210mi.

X = 210 / t.

Eq2: d1 = (X+10)(t-2.4) = 210mi.

In Eq2, substitute 210/t for X:

(210/t+10)(t-2.4) = 210,

210-504/t+10t-24 = 210,

-504/t+10t-24 = 210-210,

-504/t+10t-24 = 0,

Multiply both sides by t:

10t^2-24t-504 = 0,

Divide both sides by 2:

5t^2-12t-252 = 0.

Solve using Quadratic Formula and get:

t = 8.4, and -6. Select positive t.

t = 8.4h.

X = 210/t = 210 / 8.4 = 25mi/h.

X+10 = 25+10 = 35mi/h = Rate of 1st cyclist.

## Answer This Question

## Related Questions

- math - What would be the answer to85x205=960x3256 85 x 205 = 17425 960 x 3256 = ...
- math - A hare is in a 100m race. it starts the race at a particular speed s. ...
- algebra1 - a cyclist completes a 150-mile race in a certain amount of time.she ...
- Algebraic Geometry - A 33 kilometer bicycle race course is designed in the ...
- Math - Kyle is training for a bike race. He rides 5 miles one day, 10 miles the ...
- Physics - 1. A rabbit and a turtle are practicing for their big race. The rabbit...
- History/Literature/English - July 14, Bastille Day was the day: a) the ...
- math - The students in Mr. Stevens class are having a turtle race. The race will...
- math - The students in Mr. Stevens class are having a turtle race. The race will...
- History - How did the french respond when the U.S. refused to repay debts owed ...

More Related Questions