Two hikers are 44 miles apart and walking toward each other. They meet in 10 hours. Find the rate of each hiker if one hiker walks 2.2 mph faster than the other.
This is a distance, rate, time problem.
Distance = rate x time d = rt {d is distance, r is rate, t is time} One hiker rate = r {rate of one hiker is unknown} time = 10 {they each hike for 10 hours} distance = 10r {distance = rate x time} d = 10r Other hiker rate = r + 2.2 {one hiker walks 2.2 mph faster than the other} time = 10 {they each hike for 10 hours} distance = 10(r + 2.2) = 10r + 22 {distance = rate x time….used distributive property} d = 10r + 22 Since they are 44 miles apart, add their distances together and set equal to 44, because their combined distance is 44 miles. Then, solve for r to find the rate of one hiker, and then evaluate r + 2.2 for the rate of the other hiker. 10r + 10r + 22 = 44 {added the distances together and set equal to 44} 20r + 22 = 44 {combined like terms} 20r = 22 {subtracted 22 from each side} r = 1.1 {divided each side by 20} Substitute 1.1, in for r, into r + 2.2. r + 2.2 = 1.1 + 2.2 {substituted} = 3.3 {added} The rate of one hiker is 1.1 The rate of the other hiker is 3.3. Ask Algebra House
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