Bret started ono a 70-mile bycicle ride at 20 miles per hour. after a time he became a little tired and slowed down to 12 miles per hour for the rest of the trip. the entire trip of 70 miles took 4.5 hours. how far had bret ridden when he reduced his speed to 12 miles per hour?

Givens

Total distance = 70 miles

Distance to slowdown = x

Distance the rest of the way = y

Larger speed = 20 mph

Resting speed = 12 mph

Total Time = 4.5 hours.

Problem: solve for x

Formulas

Distance Formula: x  + y = 70

Time Formula: x/20 + y/12 = 4.5 you are asked for x.

Solution

Get rid of the fractions in the distance formula. Multiply through by 60 which is the lowest common denominator of 12 and 20.

60[x/20 + y/12 = 4.5]

3x + 5y = 270                Now substitute for y

3x + 5*(70 - x) = 270

3x + 350 - 5x = 270     Combine the xs

- 2x + 350 = 270           Subtract 350 from both sides.

-2x = 280 - 370

-2x = -80

x = -80/-2

x = 40

So Bret goes 40 miles before slowing down.

the answer is 62