The Cunninghams are moving across the country. Mr. Cunningham leaves 3.5 hours before Mrs. Cunningham. If he averages 50 mph and she averages 70 mph, how long will it take Mrs. Cunningham to overtake Mr. Cunningham?

2 Answers
May 3, 2018

Mrs Cunningham will take # 8# hour #45# minutes to overtake Mr Cunningham

Explanation:

Mr Cunningham is ahead of #d=50*3.5 = 175 # miles when

Mrs Cunningham started.

Mrs Cunningham makes up #s= (70-50)=20# miles per hour.

Therefore Mrs Cunningham will take #t=d/s= 175/20= 8.75 # hr.

i.e # 8# hour #45# minutes to overtake Mr Cunningham [Ans]

May 3, 2018

She will overtake him after #8# hours and #45# minutes

Explanation:

At the point where Mrs Cunningham overtakes Mr Cunningham, the distance they have travelled will be the same.

#D= s xx t#

Let the time for Mrs C be #(t)#

Mrs C: #"Distance" = 70 xx t = 70t#

Mr C will have taken #3.5# hours longer to cover the same distance.

Mr C: #"Distance" = 50 xx (t+3.5) = 50t +175#

the distances travelled are the same

#70t = 50t +175#

#20t = 175#

#t = 175/20#

#t = 8.75# hours

#t = 8 3/4# hours

She will overtake him after #8# hours and #45# minutes