Question

jordan and kevin are both driving along the same highway in two different cars to a stadium in a distant city. at noon, jordan is 366 miles away from the stadium and kevin is 394 miles away from the stadium. jordan is driving along the highway at a speed of 47 miles per hour and kevin is driving at speed of 54 miles per hour. let ( j ) represent jordan’s distance, in miles, away from the stadium ( t ) hours after noon. let ( k ) represent kevin’s distance, in miles, away from the stadium ( t ) hours after noon. write an equation for each situation, in terms of ( t ), and determine how far both jordan and kevin are from the stadium at the moment they are an equal distance from the stadium.

answer attempt 1 out of 2

( j = square ) ( k = square )

answer: (square)

Explanation:

Step1: Equation for Jordan's distance

Jordan starts 366 miles from the stadium and drives towards it at 47 mph. So distance from stadium decreases by 47t each hour.
$J = 366 - 47t$

Step2: Equation for Kevin's distance

Kevin starts 394 miles from the stadium and drives towards it at 54 mph. So distance from stadium decreases by 54t each hour.
$K = 394 - 54t$

Step3: Find t when J = K

Set $366 - 47t = 394 - 54t$
Add 54t to both sides: $366 + 7t = 394$
Subtract 366: $7t = 28$
Divide by 7: $t = 4$

Step4: Find distance at t = 4

Use J (or K): $J = 366 - 47(4) = 366 - 188 = 178$

Answer:

$J = 366 - 47t$
$K = 394 - 54t$