Math plz help me and show how you got your answer

Question

Sarah wanted to catch Jim. However, although they started at the same time, Jim traveled at 80 km/h and Sarah traveled at 120 km/h. How much of a head start did Jim have if it took three hours for Sarah to catch him?

Answer 1

Hi Caleb!

Since Sarah traveled 120km/h for 3 hours, using Distance = Speed X time we get that Distance =120*3, which is 360km.

Sarah traveled 360km.

Jim started earlier but we don't know by how much, that is what the question is asking. We know he went more than 3 hours because Sarah left after him and went 3 hours before she caught up to him. So Jim's time will be "t+3". Jim's speed was 80km/h. So Distance = Speed *Time gives us Distance = 80*(t+3). We know Sarah and Jim went the same distance. So we can set Jim's distance 80(t+3) equal to Sarah's distance of 360km.

Now we have:

80(t+3) = 360

Now we distribute the 80 to the t and the 3 and get:

80t + 240=360

Next, we subtract 120 from both sides:

80t = 120

Finally, we divide both sides by 80

t=1.5

We get t=1.5, so that means Jim had a head start of 1.5 hours.

Jim's total time traveling was 1.5 + 3 which equals 4.5.

But the question only asks for how much of head start Jim had, which is 1.5 hours.

Hope this helps!

80 =

Answer 2

t represents Sarah's time

t + 3 represents Jim's time

120t = 80(t + 3)

Can you solve for t and answer?