Basic Mathematics for College Students

1.6 Problem Solving 71

EXAMPLE (^3) Tunneling A tunnel boring machine can drill through
solid rock at a rate of 33 feet per day. How many days will it take the machine to
tunnel through 7,920 feet of solid rock?
Self Check 3
OIL WELLS An offshore oil
drilling rig can drill through the
ocean floor at a rate of 17 feet
per hour. How many hours will it
take the machine to drill 578 feet
to reach a pocket of crude oil?
Now TryProblem 21
AP Image
Analyze

• The tunneling machine drills through 33 feet of solid rock per day. Given


• The machine has to tunnel through 7,920 feet of solid rock. Given


• How many days will it take the machine to tunnel that far? Find

In the diagram below, we see that the daily tunneling separates a distance of 7,920
feet into equal-sized lengths of 33 feet. That indicates division.

7,920 ft

33 ft 33 ft 33 ft 33 ft

Form We translate the words of the problem to numbers and symbols.

is equal to divided by

7,920 33

SolveUse long division to find 7,92033.

 

The number of

days it takes to

drill the tunnel

the distance

that the machine

drills each day.

the length of

the tunnel

The number of

days it takes to

drill the tunnel

A diagram is often helpful when analyzing the problem.