Question

Jack takes 2 hours to drive from A to B. If he increases the speed by 25% for the return journey, how long will he take for the return journey

Answer 1

To solve this problem, let's start by determining the speed Jack drives from A to B.

Let the distance from A to B be \(d\) and let his original speed be \(v\).

From the information given, we know that:

\[
\text{Time} = \text{Distance} / \text{Speed}
\]

Thus, for the journey from A to B:

\[
2 \text{ hours} = \frac{d}{v}
\]

From this, we can express the distance \(d\) in terms of speed \(v\):

\[
d = 2v
\]

Now, Jack increases his speed by 25% for the return journey. His new speed \(v_{\text{new}}\) will be:

\[
v_{\text{new}} = v + 0.25v = 1.25v
\]

Now we can find the time taken for the return journey from B to A using the new speed \(v_{\text{new}}\):

\[
\text{Time for return journey} = \frac{d}{v_{\text{new}}}
\]

Substituting the expressions we've established:

\[
\text{Time for return journey} = \frac{d}{1.25v}
\]

Substituting \(d = 2v\):

\[
\text{Time for return journey} = \frac{2v}{1.25v}
\]

The \(v\) terms cancel out:

\[
\text{Time for return journey} = \frac{2}{1.25}
\]

Calculating \( \frac{2}{1.25} \):

\[
\text{Time for return journey} = \frac{2 \times 100}{1.25 \times 100} = \frac{200}{125} = \frac{8}{5} = 1.6 \text{ hours}
\]

Thus, the time Jack will take for the return journey is:

\[
\boxed{1.6} \text{ hours} \text{ (or 1 hour and 36 minutes).}
\]