HEEEEEEELP ME PLEASE!!!! I'll give brainliest!!!! Allie and Samuel are rock climbing. Allie climbs 5 1/2 meters in the first 1/4 hour. Samuel climbs 14 1/4 meters in the first 3/4 hour. Each persons rate stays the same for the first hour they climb. After the first hour, Samuel and Allie agree they will continue to climb up the rock face for another 1/2 hour. Allie continues to climb at the same rate. What rate must Samuel climb in the last 1/2 hour to reach the same height as Allie? Explain your thinking.
Answers
Given :- Allie and Samuel are rock climbing. Allie climbs 5 1/2 meters in the first 1/4 hour. Samuel climbs 14 1/4 meters in the first 3/4 hour. Each persons rate stays the same for the first hour they climb. After the first hour, Samuel and Allie agree they will continue to climb up the rock face for another 1/2 hour. Allie continues to climb at the same rate. What rate must Samuel climb in the last 1/2 hour to reach the same height as Allie ?
Solution :-
given that,
→ Allie climbs in (1/4) hour = 5(1/2) m = (11/2) m
So,
→ Allie climbs in 1 hour = (11/2) * 4 = 22 m .
Similarly,
→ Samuel climbs in (3/4) hour = 14(1/4) m = (57/4) m
So,
→ Samuel climbs in 1 hour = (57/4) * (4/3) = 19 m .
then,
→ after first hour allie was at = 22 m .
→ after first hour samuel was at = 19 m .
now, allie climb for same rate for (1/2) hour.
So,
→ allie will cover in half hour = (22/2) = 11 m.
and, in order to reach the same height as allie samual now has to climb = 11 + (22 - 19) = 14 m. { he was 2 m behind . }
therefore,
→ Speed of samuel = (Distance coverd) / (Time) = 14 / (1/2) = 14 * 2 = 28 m / hour.
Hence, Samuel must climb at the rate of 28 metre per hour in the last 1/2 hour to reach the same height as Allie .
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