Henry Ernest Dudeney/Puzzles and Curious Problems/76 - How Far Was It/Solution
Jump to navigation
Jump to search
Puzzles and Curious Problems by Henry Ernest Dudeney: $76$
- How Far Was It?
- "The steamer," remarked one of our officers home from the East, "was able to go twenty miles an hour down-stream,
- but could only do fifteen miles an hour upstream.
- So, of course, she took five hours longer in coming up than in going down."
- One could not resist working out mentally the distance from point to point.
- What was it?
Solution
- $300$ miles.
Proof
Let $D$ be the distance travelled.
Let $T$ be the time taken to travel $D$ downstream.
We have:
\(\ds D\) | \(=\) | \(\ds 20 T\) | The steamer was able to go twenty miles an hour down-stream | |||||||||||
\(\ds D\) | \(=\) | \(\ds 15 \paren {T + 5}\) | but could only do fifteen miles an hour upstream. So, of course, she took five hours longer in coming up than in going down. | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds 5 T\) | \(=\) | \(\ds 75\) | eliminating $D$ and simplifying | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds T\) | \(=\) | \(\ds 15\) | simplifying | ||||||||||
\(\ds \leadsto \ \ \) | \(\ds D\) | \(=\) | \(\ds 20 \times 15\) | substituting for $T$ | ||||||||||
\(\ds \) | \(=\) | \(\ds 300\) | simplifying |
$\blacksquare$
Sources
- 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Solutions: $76$. -- How Far Was It?
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $90$. How Far Was It?