If we let r be the rate Isabella rakes, then 3r is the rate at which Matthew rakes. For a unit job, their combined rate is r+3r=4r. Since a unit job took 7 hours, the time it takes for the combined effort is 7/4 hours.
It will take them 7/4 hours or 1 hour and 45minutes to finish the raking.
** To make this concrete, suppose the area to be raked is 28 square meters....
If we let r be the rate Isabella rakes, then 3r is the rate at which Matthew rakes. For a unit job, their combined rate is r+3r=4r. Since a unit job took 7 hours, the time it takes for the combined effort is 7/4 hours.
It will take them 7/4 hours or 1 hour and 45minutes to finish the raking.
** To make this concrete, suppose the area to be raked is 28 square meters. Since Isabella can finish the job in 7 hours, she rakes 4 square meters per hour. Now Matthew is three times as fast, so he rakes at 12 square meters per hour. Together they rake 4+12=16 square meters per hour. Since the job is 28 square meters, the time required is 28/16=7/4 hours as above.
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