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Kelsey can ride her bike 18 mph18\,\text{mph} and Brynn can walk 6 mph6\,\text{mph}. Brynn starts walking 22 hours before Kelsey. How long after Kelsey starts riding will they meet if they travel the same direction?\newlineHow far apart will they be?\newline

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Q. Kelsey can ride her bike 18 mph18\,\text{mph} and Brynn can walk 6 mph6\,\text{mph}. Brynn starts walking 22 hours before Kelsey. How long after Kelsey starts riding will they meet if they travel the same direction?\newlineHow far apart will they be?\newline
  1. Calculate Head Start Distance: Calculate the head start distance Brynn has after walking for 22 hours at 66 mph.\newlineDistance = Speed ×\times Time\newline= 66 mph ×\times 22 hours\newline= 1212 miles
  2. Determine Relative Speed: Determine the relative speed between Kelsey and Brynn since they are moving in the same direction.\newlineRelative Speed = Kelsey's Speed - Brynn's Speed\newline= 18 mph−6 mph18 \, \text{mph} - 6 \, \text{mph}\newline= 12 mph12 \, \text{mph}
  3. Calculate Time to Catch Up: Calculate the time it takes for Kelsey to catch up to Brynn.\newlineTime =DistanceRelative Speed= \frac{\text{Distance}}{\text{Relative Speed}}\newline=12 miles12 mph= \frac{12 \, \text{miles}}{12 \, \text{mph}}\newline=1 hour= 1 \, \text{hour}
  4. Calculate Distance Kelsey Travels: Calculate the distance Kelsey travels in the time it takes to catch up.\newlineDistance = Speed ×\times Time\newline= 1818 mph ×\times 11 hour\newline= 1818 miles

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