Uniform motion

Question

two trains going in opposite directions leave at the same time. rain B travels 15mph faster than train A. n 7 hours the trains are 875 miles apart. Find the speed of each. 

Answer 1

1. it seems beneficial to use vectors for this problem. (Remember, velocity is a vector, but speed is a magnitude.)

2. let r_b = the velocity of Train B and r_a = the velocity of Train A.

3. the absolute value of (r_b) = the absolute value of (r_a) + 15

4. s_b, the speed of B, = s_a + 15

5. now, let's use the displacement formula (d = rt)

6. d_b = (15 + s_a)*7 and d_a = s_a*7

7. d_b - d_a = 875

8. let's say d_b is traveling in the positive direction whereas d_a is traveling in the negative direction.

9. therefore, (15 + s_a)*7 - (-s_a*7) = (15 + s_a)*7 + s_a*7 = 875

10. 15 + s_a + s_a = 875/7

11. 15 + 2*s_a = 125

12. 2*s_a = 110

13. s_a = 55

14. s_b = 55 + 15

 

The speed of Train A is 55 mph, and the speed of Train B is 70 mph. 

 

Answer 2

There speed of going apart is 875/7 mi/hr=125 mi/hr

@ 15 mi/hr extra speed train B has traveled in 7 hrs = 105 miles

thus if the trains were traveling at equal speed, in 7 hrs they would have been apart by= (875-105)mi=770mi

therefore their speed of going apart would have been = 770/7 mi/hr= 110 mi/hr

therefore each of them would have traveled at speed = 110/2 mi/hr =55 mi/hr

Thus train A has a speed of 55 mi/hr and B has a speed of 70 mi/hr.