Solve the following problem.
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
DISTANCE PROBLEM
Question:
Remember:
======================
Representation:
illustration:
SOLUTION
First condition:
Second condition:
D = (t-5) (r+5) substitute the value of r
84 = (t-5) (84/t + 5)
84 = 84 +5t - 420/t - 25
84 = 5t - 420/t +59
84-59 = 5t - 420/t
25 = 5t - 420/t
t(25) = (5t-420/r)t
25r = 5t²-420
0 = 5t²-25t-420
0 = 5(t²-5t-84)
0 = 5(t-12)(t+7)
0 = t-12 , 0=t+7
12 = t , -7 = t
Logical root will be t=12
====================================
Checking
Substitute the value of r to the first equation:
Now, In the first condition:
Checking for the second condition:
ANSWER
#CarryOnLearning
Representation :
Let 84 km= distance he travelled
t hours =time he travelled
t-5 hours= time be would have travelled if his speed is 5 kph more
kph= his speed
+ 5 = what would have been his speed if he could travel 5 hours less
Illustration:
Distance÷Time = Speed
84÷(t-5)= + 5
Solution:
84÷(t-5)= + 5
Write the division as a fraction.
Write the five as a fraction
Cross-Multiply it
84t= (t-5)(84+5t)
84t= 84t+5t²-420-25t
84t= 5t²+59t-420
5t²+59t-420-84t=0
5t²-25t-420=0
(5t²-25t-420)÷5 =0÷5
t²-5t-84=0
(t+7)(t-12)=0
t+7=0 ; t-12=0
t= -7 ; t=12
The time he travelled is 12 hours.
84÷12=7
His speed is 7 kph.
Check:
84÷(t-5)= + 5
84÷(12-5)= + 5
84÷7= 7+5
12=12
84÷7=12 hours
7+5=12
84÷12=7 hours
12 hours in his original speed and 7 hours in his speed which is 5 kph more has a difference of 5 hours.