Question

The average distance that Ben and Tina drove was 153 kilometres. If Bendrove 24 kilometres more than Tina, what was the distance that Ting drove? ​

Answer 1

$\sf\large\underline{Let:}$

• $\rm{Distance\: covered\:by\:Ben=B\:km}$
• $\rm{Distance\: covered\:by\:Tina=T\:km}$

$\sf\large\underline{To\: Find:}$

• $\rm{The\: distance\: covered\:by\:Tina=?}$

$\sf\underline{Given\:in\:case\:(i):}$

$\tt{The\:average\:distance\:that\:Ben\:and\:Tina\:drove\:was\: 153km}$

$\rm{\implies Average\:_{(distance\:of\:B\:and\:T)}=Total\:_{(distance)}}$

$\rm{\implies \dfrac{B+T}{2}=153}$

$\rm{\implies B+T=306-----(i)}$

$\sf\underline{Given\:in\:case\:(ii):}$

$\tt{Ben\:drove\:24\:km\:more\:than\:Tina}$

$\rm{\implies B=T+24------(ii)}$

• Putting the value of B=T+24 in eq (i) here]

$\rm{\implies B+T=306}$

$\rm{\implies T+24+T=306}$

$\rm{\implies 2T+24=306}$

$\rm{\implies 2T=306-24}$

$\rm{\implies 2T=282}$

$\rm{\implies T=141}$

• Now, putting the value of T=141 in eq (ii) ]

$\rm{\implies B=T+24}$

$\rm{\implies B=141+24}$

$\rm{\implies B=165}$

$\sf\large{Hence,}$

$\rm{\implies Ben\:_{(covered\: distance)}=165\:km}$

$\rm{\implies Tina\:_{(covered\: distance)}=141\:km}$

Answer 2

Given:

The average distance that Ben and Tina drove was 153

=>x+y/2=153

=>x+y=306------(I)

Bendrove 24 kilometres more than Tina,

x=y+24-----(ii)

substituting value here

=>x+y=306

=>y+24+y=306

=>2y+24=306

=>2y=306-24

=>2y=282

=>y=141km

therefore, Tina drove =141km