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Chapter 2: Q. 18 (page 120)

Two cars leave an intersection at the same time. One is headed south at a constant speed of 30 miles per hour, and the other is headed west at a constant speed of40 miles per hour (see the figure). Build a model that expresses the distance between the cars as a function of the time t.

[Hint: At t=0, the cars leave the intersection.]

Short Answer

Expert verified

The distance d between the cars as a function of the time tis 50t.

Step by step solution

01

Step 1. Find the equations for the distance travelled by both cars.

The distance travelled by first car in time t is 30t.

The distance travelled by the second car in time t is 40t.

02

Step 2. Apply Pythagorean theorem in the following figure.

d(t)=(30t)2+(40t)2=900t2+1600t2=2500t2=50t

So the distance d between the cars as a function of the time tis 50t.

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