Question

What is the distance between Harry’s home and his office?

(1) Harry’s average speed on his commute to work this Monday was 30 miles per hour.
(2) If Harry’s average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.

Answer 1

Answer:

The distance between Harry’s home and his office? is 15 miles.

Step-by-step explanation:

The speed, distance time formula is:

$Speed(s)=\frac{Distance(d)}{Time(t)}$

Given:

Speed (s) = 30 miles/hour

Then the relation between distance and time is:

$s=\frac{d}{t} \\30=\frac{d}{t}\\d=30t...(i)$

If Speed was 60 miles/hour the time taken is $(t-\frac{1}{4})$ hours.

Then the relation between distance and time is:

$s=\frac{d}{t} \\60=\frac{d}{(t-\frac{1}{4}) }\\d=60t-15...(ii)$

Use the value of d = 30t in (ii)

$d=60t-15\\30t=60t-15\\30t=15\\t=\frac{1}{2} hour$

Determine the distance as follows:

$d=30t\\=30\times\frac{1}{2} \\=15\ miles$

Thus, the distance between Harry’s home and his office? is 15 miles.