Question

Match the following equations showing the time taken by 3 students to reach school with their correct results:

• A. 5.2 minutes
• B. 18 minutes
• C. 10 minutes

Answer 1

Given:

Time taken by first student,
$\text{15(3 + t) + 5t = 25t - 45}$

$⟹\text{45 + 15t + 5t = 25t - 45}$
(Using distributive property)

$⟹\text{45 + 45 = 25t - 15t - 5t}$
(Rearrange the like terms)

$⟹\text{90 = 25t - 20t}$

$⟹\text{90 = 5t}$

$⟹\frac{90}{5}=\text{t}$
(Dividing with 5 on both sides)

$⟹\text{t}=18$

Time taken by first student is 18 minutes.


Given:

Time taken by second student,
$\frac{\text{t - 72}}{\text{2t - 3}}+6=\frac{\text{2t - 2}}{\text{2t - 3}}-4$

$⟹\text{t - 72}+6\left(\text{2t - 3}\right)=\text{2t - 2}-4\left(\text{2t - 3}\right)$
(Taking 2t - 3 as L.C.M)

$⟹\text{t - 72}+\text{12t - 18}=\text{2t - 2}-\text{8t + 12}$
(Uisng distributive property)

$⟹\text{t +12t - 2t + 8t}=-2+12+72+18$
(Rearrange the like terms)

$⟹\text{19t}=100$

$⟹\text{t}=5.2$
(Dividing 19 on both sides)

The time taken by the second student is 5.2 minutes.


Given:
Time taken by third studen
$\frac{5}{3}\text{(t - 6)}=\frac{\text{t - 2}}{3}+4$

$⟹5\text{(t - 6)}=\text{t - 2}+4\times 3$
(Taking 3 as L.C.M)

$⟹\text{5t - 30}=\text{t - 2}+12$
(Uisng distributive property)

$⟹\text{5t - t}=-2+12+30$
(Rearrange the like terms)

$⟹\text{4t}=40$

$⟹\text{t}=10$

(Dividing 4 on both sides)

Time taken by third student is 10 minutes.