Question

Jack and Jill live 126 km apart. They want to leave their homes at the same time,
ride their bikes toward each other, meet for lunch at 12:00 PM, and then go climb
a hill. Jack rides 18 kilometers per hour. Jill rides 24 kilometers per hour. What is
the latest time they can leave their houses and meet on time?

Answer 1

Answer:

Both will leave their homes to meet on time at 9 am  

Step-by-step explanation:

Given as, Distance between Jack  and Jill = 126 km

Speed of Jack rides = 18 kilometers per hours

Speed of Jill rides     = 24 kilometers per hours

Let the distance travel by Jack = x km

And the distance travel by Jill  =  (126 - x ) km

Time taken by Jack and Jill = T hours

Now , Distance = Speed × Time

So,     x = 18 × T

And  126 - x = 24 × T

Or,    126 - x =  24 × $\frac{x}{18}$

Or,    126 - x =  x × $\frac{4}{3}$

Or,    378 - 3x = 4x

Or,    378 = 7x

i.e x = $\frac{378}{7}$ = 54 km

And distance travel by Jill = 126 - 54 = 72 km

So, time taken by Jack = $\frac{x}{18}$ = $\frac{54}{18}$

Or, Time taken by Jack = 3 hours

Similarly Time take by Jill = $\frac{72}{24}$ = 3 hours

∵ Both Jack and Jill will take 3 hours to meet at 12 : 00 pm

Hence, Both will leave their homes to meet on time at 9 am   Answer