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# Distance Rate Time Word Problems

The speed distance time is mathematically given as
x = $\frac{d}{t}$
Where x is the Speed in m/s,d is the Distance traveled in m, t is the time taken in s.The distance formula is also given as
d = vt + $\frac{1}{2}$ at2
where d is distance traveled in a certain amount of time (t), v is starting velocity, a is acceleration (must be constant), and t is time. This gives you the distance traveled during a certain amount of time. If you know any 3 of those things, you can plug them in to solve for the 4th. So if you only know v and d, you can't solve for a unless you also know what t is (i.e. what time was d measured at).

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## Distance Word Problems

Distance word problems tells how far the body moves for a given time. Here are some problems on distance you can go through it:

### Solved Examples

Question 1: A car covers a distance of 100 m in 10 seconds. Calculate its speed.
Solution:

Given: Distance d = 100 m, time t = 10 s
The speed is given by
S = $\frac{Distance\ covered}{time\ taken}$
= $\frac{100}{10}$
= 10 m/s.

Question 2: Raja took a drive to town at an average rate of 40 mph. In the morning, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by raja?
Solution:

Let us take t = time to travel to town. And 7 – t = time to return from town.
Given: Average speed Rate = 40 and time = t, Again speed rate x = 30 m, and time = 7 - t
Using the formula d = xt
Distance d = 40 $\times$ t or d = 30 $\times$ (7 – t)
Since the distances traveled in both cases are the same, We get the equation: 40t = 30(7 – t)
Using the distributive property 40t = 210 – 30t
Isolate the variable t
40t + 30t = 210
or
70t = 210 t = $\frac{210}{70}$
t = 3s
The distance traveled by raja to town is 40t = 40 $\times$ 3 = 120
40t = 120
The distance traveled by raja to go back is also 120 So, the total distance traveled by raja is 240 miles.The distance traveled by raja is 240 miles.

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