Challenge (OPTIONAL) $\newline$ Adam, Bob, Clair and Dave come to a rickety old wooden bridge. The bridge is only able to carry the weight of two of them at a time. The light is fading, so they must carry their only flashlight on each crossing. Because of their fitness levels and some minor injuries, they cross at different speeds. $\newline$ Adam can cross in $1$ minute, Bob in $2$ minutes, Claire in $5$ minutes, and Dave in $10$ minutes. Claire declares that the crossing can be completed in less than $20$ minutes. Do you agree? Prove it!

View step-by-step help

Home

Math Problems

Grade 8

Solve proportions: word problems

Full solution

Q. Challenge (OPTIONAL)

\newline

Adam, Bob, Clair and Dave come to a rickety old wooden bridge. The bridge is only able to carry the weight of two of them at a time. The light is fading, so they must carry their only flashlight on each crossing. Because of their fitness levels and some minor injuries, they cross at different speeds.

\newline

Adam can cross in

1

minute, Bob in

2

minutes, Claire in

5

minutes, and Dave in

10

minutes. Claire declares that the crossing can be completed in less than

20

minutes. Do you agree? Prove it!

Identify Strategy: Identify the fastest way to get all four people across the bridge. $\newline$ Since only two people can cross at a time and they need the flashlight to cross, the strategy should minimize the time the slowest people take to cross and maximize the use of the fastest people.
Send Fastest Pair First: Send the two fastest people first. $\newline$ Adam and Bob cross together with the flashlight, taking $2$ minutes because they must move at the speed of the slower person. $\newline$ Time elapsed: $2$ minutes.
Send One Back: Send one of the fastest people back with the flashlight. Adam goes back with the flashlight, taking $1$ minute. Time elapsed: $2 + 1 = 3$ minutes.
Send Slowest Pair: Send the two slowest people across the bridge. $\newline$ Clair and Dave cross together with the flashlight, taking $10$ minutes because they must move at the speed of the slower person. $\newline$ Time elapsed: $3 + 10 = 13$ minutes.
Send Fastest Back: Send the fastest person who is on the starting side back across with the flashlight. $\newline$ Bob goes back with the flashlight, taking $2$ minutes. $\newline$ Time elapsed: $13 + 2 = 15$ minutes.
Send Fastest Pair Again: Send the two fastest people across the bridge again. $\newline$ Adam and Bob cross together with the flashlight for the last time, taking $2$ minutes. $\newline$ Time elapsed: $15 + 2 = 17$ minutes.