Math 99 beginning Algebra

Question

The sum of the speeds of two trains is 722 3 miles per hour. If the speed of the first train is 7.7 mph faster than that of the second train, find the speeds of each What is the speed of the first train?

Answer 1

designate the speed of the first train X. The speed of the second train is.X - 7.7 (if first train is 7.7 miles per hour faster, then second train is 7.7 miles slower). Add the two speeds and put them equal to 722.3.

X + X - 7.7 = 722.3; 2X - 7.7 = 722.3; add 7.7 to both sides; 2X = 730; divide by 2; X = 365

Answer 2

Let x = speed of first train

y = speed of second train

The sum of the speeds is 722.3, so x +y = 722.3

But since the first train's speed is 7.7 more than that of the second train, the first train's speed can be represented by y + 7.7, so x = y + 7.7

In the equation x + y = 722.3, substitute y + 7.7 for the speed of the first train:

(y + 7.7) + y = 722.3

Solve algebraically, first by combining like terms:

2y +7.7 = 722.3

2y = 714.6

y = 357.3

The speed of the second train, y, is 357.3 mph, and the speed of the first train, x, is 357.3 + 7.7 = 365 mph.

Always check your work by plugging your answers into the original equation:

x + y = 722.3

365 +357.3 = 722.3

Hope this helps!

Nancy

Answer 3

From the problem you listed above, you get the following :

V_T1 = Velocity of Train 1

V_T2 = Velocity of Train 2

V_T1 + V_T2 = 722.3

V_T1 = V_T2 + 7.7

Plug the 2nd equation into the first & solve :

V_T1 + V_T2 = 722.3

(V_T2 + 7.7) + V_T2 = 722.3

7.7 + 2*V_T2 = 722.3

2*V_T2 = 714.6

V_T2 = 357.3

Plug V_T2 into the 2nd equation and solve :

V_T1 = V_T2 + 7.7

V_T1 = 357.3 + 7.7

V_T1 = 365

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Always check your work

V_T1 + V_T2 = 722.3

365 + 357.3 = 722.3

722.3 = 722.3

V_T1 = V_T2 + 7.7

365 = 357.3 + 7.7

365 = 365

Correct!