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Time and Distance Ratios Examples
In this class, We discuss Time and Distance Ratios Examples.
The reader should have prior knowledge of the time and distance formula. Click Here.
Example 1:
A certain distance is covered by a bike at a certain speed, and
if the cyclist covers half the distance in double the time.
The ratio of speeds of cyclists to that of a bike?
Solution:
Assume, Distance = D
Bike:
Speed = x
Time = Distance / Speed
t = D/x
Cyclist:
2t = (d/2)/y
Speed of cycle = y
y = d/4t
y : x = (d/4t) : (d/t)
y : x = 1 : 4
Important: when they ask for ratios, we can cancel the distance and time. This point should come to your mind.
Example 2:
Three persons are walking from place A to Place B.
Their speeds are in the ratio of 4 : 3: 5.
The ratio of their times is?
Solution:
From the formulas discussed, the ratio of times is inversely proportional to speeds if the equal distance traveled.
1/4: 1/3: 1/5
60/4: 60/3: 60/5
15: 20: 12
Example 3:
A dog takes four leaps for every five leaps of the rabbit.
Three leaps of the dog are equal to 5 leaps of the rabbit.
Find the ratio of speeds?
Solution:
A dog takes four leaps for every five leaps of the rabbit.
In the above statement, we must understand that the dog takes four leaps at a certain time t, and the rabbit takes five leaps.
Three leaps of the dog = five leaps of the rabbit.
From the above statement, we have to understand the size of the leaps is different.
Dog leap is big when compared to rabbit leap.
The below diagram shows the leaps.
Assume dog leap distance = x
rabbit leap distance = y
3x = 4y
x = 4y/3
The dog takes four leaps for every five leaps of the rabbit. so 4x = 5y
The ratio of speeds is directly proportional to distance if times are the same.
We made the above statement from the formulas discussed.
s1 : s2 = 4x : 5y
s1 : s2 = 4(4y/3) : 5y
16y/3: 5y
s1 : s2 = 16 : 15

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