Question

write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
a couple of friends decide to race each other. manny can run 5 meters per second, whereas tommy can run 6 meters per second. because he is slower, manny also gets a head start of 29 meters. shortly after they start running, tommy will catch up to manny. how far will tommy have to run? how long will that take?
tommy will catch up to manny after running (square) meters in (square) seconds.
submit

Explanation:

Step1: Define variables

Let $t$ = time (seconds) until Tommy catches Manny, $d_T$ = distance Tommy runs, $d_M$ = distance Manny runs.

Step2: Set up distance equations

Tommy: $d_T = 6t$
Manny: $d_M = 5t + 29$

Step3: Set distances equal (catch up)

$$6t = 5t + 29$$

Step4: Solve for $t$

Subtract $5t$ from both sides:
$6t - 5t = 29$
$t = 29$

Step5: Find Tommy's distance

Substitute $t=29$ into $d_T=6t$:
$d_T = 6 \times 29 = 174$

Answer:

Tommy will catch up to Manny after running 174 meters in 29 seconds.