A charter bus travels 210 miles in 3 1/2 hours. assume the distance traveled is directly proportional to the time traveled. write and solve a direct variation equation to find how far the bus travel in 6 hours.

The constant of variation is 60 miles.

Direct variation formula: y = kx

y = 210

x = 3 1/2 miles

k = ?

k = y/x

k = 210 / 3 1/2 miles

*convert mixed fraction into a simple fraction

3 1/2 = (3*2+1) / 2 = 7/2

k = 210 : 7/2

Remember the rule of dividing fractions: multiply the 1st fraction by the reciprocal of the 2nd fraction.

1st fraction = 210 ⇒ 210/1

2nd fraction = 7/2 ⇒ reciprocal = 2/7

k = 210/1 * 2/7 = (210*2) / (1*7) = 420/7 = 60

The constant of variation is 60 miles.

To check:

y = kx

y = 60 (3.5)

y = 210 miles