Question

Shen drove 603 miles in 9 hours. At the same rate, how long would it take him to drive 335 miles?

Answer 1

5 hours

Explanation:

Since Shen drove at the same rate for both distances, we can use a proportion to solve for the time it would take him to drive 335 miles:

`(d_(1) )/(t_(1) )=(d_(2) )/(t_(2) )`

where d1 is 603 miles, t1 is 9 hours, d2 is 335, and t2 is the unknown value.

Thus, we can simply plug in everything to the equation and solve for t2:

`(603)/(9)=(335)/(t_(2) )\\ 67=(335)/(t_(2) )\\ 67t_(2)=335\\ t_(2)=5`

(*Note that 9 divides evenly into 603 and becomes 67, which is why I didn't cross-multiply first with he 603 and t2 and the 335 and 9, although you'd still get the same result for t2)

Thus, it would take Shen 5 hours to drive 335 miles.

You can check by finding the rate for both equations since we know that distance is equal to the product of rate and time (d = rt):

First equation: 603 miles = 9 hours * r mph

67 mph = r

603 = 67 * 9

Second equation: 335 miles = 5 hr * r mph

67 mph = r

335 = 67 * 5