drive to work

Question

Bob drove from home to work at
75
mph. After work the traffic was? heavier, and he drove home at
60
mph. His driving time to and from work was
1
hour and
21
minutes. How far does he live from his? job?

Answer 1

Jessica,

 

Let t₁ be the time it takes Bob to drive to work and t₂ the time it takes to drive home.  Then, the total drive time is:

 

(1) t₁ + t₂ = 1 hour and 21 minutes = 1.35hours (21 minutes is .35 hours)

 

We also know that the distance Bob drives to work is the same distance he drives home.  So:

 

(2) d₁ = d₂

 

The general form for distance given a velocity is:

 

d = vt

 

For the drive to work, then:

 

d₁ = 75t₁

 

For the drive home:

 

d₂ = 60t₂

 

We can substitute these values for d₁ and d₂ into (2):

 

(3) 75t₁ = 60t₂

 

Now, rewrite (1) in terms of one of the variables (we'll use t₁₎:

 

t₁ + t₂ = 1.35

 

t₁ = 1.35 - t₂ (subtract t₂ from both sides)

 

Use this value of t₁ in (3):

 

75(1.35 - t₂) = 60t₂

 

101.25 - 75t₂ = 60t₂

 

Add 75t₂ to both sides:

 

101.25 = 135t₂

 

Divide both sides by 135:

 

.75 = t₂ (the drive home takes .75 hours or 45 minutes)

 

To find the distance he travels, use:

 

d₂ = 60 * .75

 

d₂ = 45 miles (which is the same distance as d₁)