Algebra 1 Practice Test - Linear Equations and Systems

Question

Easton is 200 miles east of Weston. Thomas the Tank Engine leaves Easton at 2:00PM

traveling west at 40 miles per hour (mph). At the same time, James the Red Engine leaves

Weston traveling east at 55 miles per hour.

1) Write an equation which represents Thomas’s distance from Easton as a function of the

time in hours since he left.

_________________________________________

2) Write an equation which represents James’s distance from Easton as a function of the

time in hours since he left.

_________________________________________

3) At what time do the trains collide? (Round to the nearest minute) _______________

4) How far are the trains from Weston when they collide? _______________________

The next day, James is running late. Thomas leaves at the same time with the same speed and

direction as the day before. James travels with the same speed and direction, but leaves some

time later than 2:00PM. The trains collide exactly halfway between the two cities.

5) What time did James leave Weston? (Round to the nearest minute? ______________

Answer 1

1) thomas' distance = 40t where t = hours

2) james' distance =200- 55t

3) 4:06 pm

200 = (40+55)t

t=200/95= 40/19= about 2 hours and 6 minutes to collide = 4:06 pm

4) 115.5 miles

55x 40/19 = 220/19 = about 55x2.1 = 115.5 miles from weston when colliding

if they collided halfway then james left later than 2 pm

5) time james left

thomas left at 2pm going 100 miles in 2,5 hours

100=40t

t= 2.5 hours =2+2.5 = 4:30 pm collision

for james

55t=100

t=100/55= 20/11=1 9/11 hours to go 100 miles

4:50 minus 1 9/11 hours = 3:01 pm when james left