Erin goes off on a long bike ride, averaging 10 km/h. One hour later her brother Alistair starts chasing after her at 16 km/h. How long will it take Alistair to catch up to Erin?

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Erin goes off on a long bike ride, averaging 10 km/h. One hour later her brother Alistair starts chasing after her at 16 km/h. How long will it take Alistair to catch up to Erin?

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Answer 1 · 2017-07-17T11:23:14

$2 hours$ $2"hours "$ 40"mins"

Explanation:

$using the calculation$ $"using the calculation"$

$∙ distance ( D ) = average speed \times time ( t )$ $• " distance ( D ) "="average speed " xx" time ( t )"$

$Erin \to D = 10 t$ $"Erin "toD=10t$

$Alistair \to D = 16 t - 16$ $"Alistair "toD=16t-16$

#"since he starts 1 hour later subtract 16 from distance"

$we require to calculate t for the same distance covered$ $"we require to calculate t for the same distance covered"$

$solve 16 t - 16 = 10 t$ $"solve "16t-16=10t$

$\Rightarrow 6 t = 16$ $rArr6t=16$

$\Rightarrow t = \frac{16}{6} = \frac{8}{3} hours = 2 hours 40 minutes$ $rArrt=16/6=8/3" hours "=2"hours " 40" minutes"$

$As a check$ $color(blue)"As a check"$

$for this time they should both have done same distance$ $"for this time they should both have done same distance"$

$Erin \to D = 10 \times \frac{8}{3} = \frac{80}{3} Km$ $"Erin "toD=10xx8/3=80/3" Km"$

$Alistair \to D = 16 \times \frac{8}{3} - 16 = \frac{128}{3} - \frac{48}{3} = \frac{80}{3} Km$ $"Alistair "toD=16xx8/3-16=128/3-48/3=80/3" Km"$

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Erin goes off on a long bike ride, averaging 10 km/h. One hour later her brother Alistair starts chasing after her at 16 km/h. How long will it take Alistair to catch up to Erin?

1 Answer

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