Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at a rate of 45 miles per hour. The westbound train travels at a rate of 55 miles per hour. How long will it take for the two trains to be 280 miles apart

2.8 hours

Step-by-step explanation:

Train A: time= t, v=45mi/hr, d= d

Train B: time t, v= 55mi/hr, d=280-d

Distance = v times t (d=vt)

t = d/v (time for both trains is the same, so t=t)

Train A: t=d/45

Train B: t=(280-d)/55

d/45 = (280-d)/55 (cross multiplication)

55d = 15400-45d

55d+45d = 15400

100d = 15400

d = 154 miles (280miles - 154miles = 126 miles)

Train A travel 154 mi and train B travel 126 mi

Train A travel 154 miles in 2.8 hrs.

Train B travel 126 miles in 2.8 hrs.

154 miles at a rate of 55mi/h = 2.8 hours and

126 miles at a rate of 45mi/h = 2.8 hr.

its the fourth option

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.