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 asd = vt + $\frac{1}{2}$ at^{2}^{}

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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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.

S = $\frac{Distance\ covered}{time\ taken}$

= $\frac{100}{10}$

= 10 m/s.

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 = $\frac{210}{70}$ s

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.