How to Calculate the Distance of a Trip with a Rest Stop and Constant Speed?

[Embison]

The question is:

A person takes a trip, driving with a constant speed 89.7 km/h except for a 21.5 min rest stop.
If the person's average speed is 70.9 km/h, how far is the trip? Answer in units of km.



I haven't done this kind of thing for years! and I was just wondering if I solved it properly.. here is what i came up with...



time = 89.7 x (t - 21.5/60) = 70.9, 89.7 t - 38.5 = 70.9 t, t = 2.70 h

distance = 70.9 x 2.70 = 191.43 km


Is that right? Any help would be greatly appreciated.

Thanks

 

[Tron3k]

Let d be the length of the trip (km). Let t be the time of the trip (hours).

$$70.9t = d$$
$$89.7(t - 21.5/60) = d$$
$$70.9t = 89.7t - 1928.55/60$$
$$18.8t = 1928.55/60$$
$$t = 1.71$$
$$d = 70.9t = 121$$

The trip was 121 km long and took 1.71 hours.

 

[Embison]

i wish i knew how you did that...

but i don't even know what / <-- means?

i think it means to divide but I've forgotten all of the math i was taught.

it's been years.

 

[HallsofIvy]

Okay, here's a "translation".

As Tron3k said "Let d be the length of the trip (km). Let t be the time of the trip (hours)."

Since the person stopped for 21.5 min.= 21.5 min/60 min/h (21.5 divided by 60)= 0.358 h, the time actually in motion (at a constant speed of 89.7 km/h) was t- 0.358 hours. Since speed is defined as "distance divided by time" we have 89.7= d/(t-0.358) or (multiply by t-0.358 to get rid of the fraction) 89.7(t-0.358)= d.

We are told that the average speed (averaging the constant 89.7 when he was moving with the 0 speed while stopped) was 70.9 km/h.
The average speed is calculated (again using "distance divided by time") using the total time: 70.9= d/t or d= 70.9t.

Since d is the same in both equations, d= 70.9t= 89.7(t- 0.358)=
89.7t- (89.7)(0.358)= 89.7t- 32.15 or
70.9t= 89.7t- 32.15

Subtract 89.7t from both sides: -18.8t= -32.15. Now divide both sides of the equation by -18.8: t= -32.15/-18.8= 1.71 hours.
(Much to my amazement, the same answer Tron3k got!)

Now put that back into either d= 89.7(t- 0.358) or d= 70.9t:
Since d= 70.9t is easier: d= 70.9(1.71)= 121 km.

 

[PrudensOptimus]

Originally posted by Embison
i wish i knew how you did that...

but i don't even know what / <-- means?

i think it means to divide but I've forgotten all of the math i was taught.

it's been years.

hahaha rofl

 

[K_go_1]

I wanted to ask how you got 18t?

 

[HallsofIvy]

I wanted to ask how you got 18t?

? What "18t"? I did get "18.8t" exactly like I said:

70.9t= 89.7t- 32.15

Subtract 89.7t from both sides

70.9t- 89.7t= (70.9- 89.7)t= -(89.7- 70.9)t= -18.8t.
That made the equation -18.8t= -32.15 so I multiplied both sides by -1:

18.8t= 32.15.

How did you find this thread? It is 7 years old!