Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 5 hours. How much time would it take for them to mow the lawn together?

Question

Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 5 hours.  How much time would it take for them to mow the lawn​ together?

Abigail Allen · Accepted Answer

Exact time taken

time is #2 2/9" hours"#
time is #2" hours "13 1/3" minutes"# There is a trick to answering this question type. Let the total amount of work to mow the lawn be #W_t# Let the work rate of jack be #w_j# Let the work rate of Marilyn be #w_m# Let the unknown time they work together be #t" hours"# Then if they do it on their own we have: #w_jxx4" hours"=W_t# #w_mxx5" hours"=W_t# So from the above the work rate of each is: #w_j=W_t/(4" hours")" " ...............Equation(1)# #w_m=W_t/(5" hours")" "..............Equation(2)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ work rate x time = Total work done So combining the two people for a given length of time we have: #color(red)([w_jxxt] )color(white)("d")+color(white)("d")color(blue)( [w_mxxt])=color(green)(W_t)" ".......Equation(3)# Using #Eqns(1) and Rqn(2)# substitute for work rate in #Eqn(3)# #color(red)([W_t/4xxt])+color(blue)([W_t/5xxt])=color(green)(W_t) " ".....Equation(3_a)# Divide everything on both sides by #W_t# #[1/4t]+[1/5t] = 1# Factor out the #t# #t[1/4+1/5]=1# #t[(5+4)/20]=1# #t=20/9 = 2 2/9" hours"# But there are 60 minutes in 1 hour so converting #2/9# hours into minute: #->2/9xx60 = 13 1/3# minutes #t=2" hours "13 1/3" minutes"#

Avery Alexander · Answer

undefined To find the time it takes for Jack and Marilyn to mow the lawn together, you can use the formula:

$$ \text{Time} = \frac{1}{\text{Rate}} $$

Where the rate is the reciprocal of the time taken to mow the lawn.

1. Calculate Jack's rate: $ \text{Rate}_{\text{Jack}} = \frac{1}{4} $ lawns per hour.
2. Calculate Marilyn's rate: $ \text{Rate}_{\text{Marilyn}} = \frac{1}{5} $ lawns per hour.
3. Add their rates to find their combined rate: $ \text{Combined Rate} = \text{Rate}_{\text{Jack}} + \text{Rate}_{\text{Marilyn}} $.
4. Find the time it takes for them to mow the lawn together using the formula above with the combined rate.

Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 5 hours. How much time would it take for them to mow the lawn​ together?

Jack usually mows his lawn in 4 hours. Marilyn can mow the same yard in 5 hours. How much time would it take for them to mow the lawn together?