To solve the word problems on speed distance time we need to know the relationship between speed (rate), distance and time.

**Speed = Distance**

** Time = Distance**

** Distance = Speed × Time**

The formula is used to solve different questions on distance covered, time taken, uniform speed and variable speed problems.

The detailed explanation will help us to understand how to solve the word problems on speed distance time.

**1.** An airplane travels 4362 km against the wind in 6 hours and 5322 km with the wind in the same amount of time. What is the rate of the plane in still air and what is the rate of the wind?

**Solution:**

Let the speed of the air plane in still air be x km/hr

And the speed of the wind be y km/hr.

Then speed of the airplane going with the wind = (x + y) km/hr

and speed of the airplane going against the wind = (x - y) km/hr.

We know that,

** Distance = Speed
× Time**

or, **Speed = Distance**

According to the problem,

An airplane travels 4362 km against the wind in 6 hours

x - y = 4362/6

or, x - y = 727 ----------- (1)

Again, the airplane travels 5322 km with the wind in the same amount of time i.e. 6 hours

x + y = 5322/6

or, x + y = 887 ----------- (2)

Now add (1) and (2) we get,

x - y = 727

__ x + y = 887__

2x = 1614

or, 2x/2 = 1614/2, (Divide both sides by 2)

or, x = 807

Now substitute the value of value of x = 807 in equation (2) we get,

807 + y = 887

__-807 -807,__ (Subtract 407 from both sides)

y = 80

**Answer:** Rate
of the plane in still air = 807 km/hr

Rate
of the wind = 80km/hr

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