Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Two kids at a summer camp, Jonah and Mabel, are competing in a potato sack race. Jonah is younger, so he is given a head start of 30 meters. When the race starts, Jonah hops at a rate of 2 meters per second, and Mabel hops 3 meters per second. Eventually, Mabel will overtake Jonah. How long will that take? How far will Mabel have to hop? It will take _____ seconds for Mabel to hop _____ meters and catch up to Jonah.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Two kids at a summer camp, Jonah and Mabel, are competing in a potato sack race. Jonah is younger, so he is given a head start of 30 meters. When the race starts, Jonah hops at a rate of 2 meters per second, and Mabel hops 3 meters per second. Eventually, Mabel will overtake Jonah. How long will that take? How far will Mabel have to hop?   It will take _____ seconds for Mabel to hop _____ meters and catch up to Jonah.

Bytelearn · Accepted Answer

Define Equations: Let's define two equations to represent the distances that Jonah and Mabel travel over time. Let t be the time in seconds after the race starts.  For Jonah, who starts 30 meters ahead and hops at a rate of 2 meters per second, the distance he travels can be represented by: D_j = 2t + 30Calculate Distances: For Mabel, who starts from the starting line and hops at a rate of 3 meters per second, the distance she travels can be represented by: D_m = 3tSet Equations Equal: We want to find the time t when Mabel catches up to Jonah. This happens when their distances are equal, so we set the two equations equal to each other: 2t + 30 = 3tSolve for Time: Now we solve for t by subtracting 2t from both sides of the equation: 2t + 30 - 2t = 3t - 2t 30 = tCalculate Mabel's Distance: We have found that it will take 30 seconds for Mabel to catch up to Jonah. Now we need to find out how far Mabel will have hopped in that time. We use Mabel's distance equation with t = 30: D_m = 3t D_m = 3(30) D_m = 90 meters

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