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