Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

A couple of friends decide to race each other. Isaiah can run 7 meters per second, whereas Brett can run 8 meters per second. Because he is slower, Isaiah also gets a head start of 21 meters. Shortly after they start running, Brett will catch up to Isaiah. How far will Brett have to run? How long will that take?

Brett will catch up to Isaiah after running _ meters in _ seconds.

Please I need help on this tomorrow I have an test on this and I kept trying to solve this but somehow I keep getting it wrong. Can anyone pls help me and show me the actual way to do it with all the steps pls. Thank you

Answer 1

8b = 21 + 7I, where b= seconds Bret ran and I=seconds Isaiah ran, or use x and y if you prefer

b=I

substitute b for I into 1st equation to get:

8b = 21 +7b

subtract 7b from both sides

8b-7b = 21

b = 21 seconds until Brett catches up to Isaiah, where Brett has gone 8x21 = 168 meters and Isaiah has gone 7x21 = 147 meters with a head start of 21 meters, 147+21 = 168

time 0, Isaiah is 21 meters ahead

time t=1, Isaiah has gone 7 meters reaching the 28 meter mark, and Bret has gone 8 meters

time t=2 Isaiah has gone 2x7 = 14 meters, at the 35 meter mark, and Bret has gone 2x8 = 16 meters

...

time t= 21 Isaiah has gone 21x7 = 147 meters reaching the 147+21 = 168 meter mark and Bret has gone 21x8 = 168 meters

it's sort of a coincidence that seconds and headstart meters are both 21