Question

Neil and Yuki run a data entry service. Neil starts at 9:00 A.M. and can type 45 words per minute. Yuki arrives at 10:30 A.M. and can type 60 words per minute. Write and solve an inequality to find at what time Yuki will have typed more words than Neil. Let x represent the time in minutes.

Answer 1

Find the number of minutes from 9.00am  to 10.30am

9.00am  to 10.30am = 1.5 hours = 90 mins

Neil can type 45 words in 1 min

⇒ 1 min = 45 words

Find the number of words typed in 90 mins:

1 min = 45 words

90 mins = 45 x 90 = 4050 words

Yuki can type 60 words in 1 min

⇒ 1 min = 60 words

Form equation for Yuki to type more than Neil

Total number of minutes typed = x

60x > 4050 + 45x

Solve x:

60x - 45x > 4050

15x > 4050

x > 4050 ÷ 15

x > 270

Find the time:

10.30am + 270 mins = 10.30am  + 4h 30 mins = 3pm

Answer: Yuki would have time more than Neil after 3pm