# Emily rows six miles downstream in 1 hour and her friend Ashley, rowing 1 mile per hour faster, completes the return trip in 2 hours. If Emily and Ash ley were rowing separately, who would...

Emily rows six miles downstream in 1 hour and her friend Ashley, rowing 1 mile per hour faster, completes the return trip in 2 hours.

If Emily and Ash ley were rowing separately, who would complete their trip first and by how long? Round to the nearest hundredth, if necessary.

speed of the current:2mph.

rowing speed of Emily.

rowing speed of Ashley.

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### 1 Answer

Emily rows downstream (with the current); she takes 1 hour to go 6 miles. The current is 2mph and Emily's total speed is 6mph (she covers 6 miles in 1 hour so 6mph) so **Emily rows at 4mph.**

**Ashley rows 1 mph faster s0 Ashley's rowing speed is 5mph.**

(Check -- rowing at 5mph **against** a current of 2mph means she travels at 3mph. Going 6 miles at 3mph requires 2 hours, which is the time given.)

Suppose that Emily and Ashley separately rowed the entire 12 mile trip -- 6 miles downstream and 6 miles back upstream.

Emily rows at 4mph. Thus her downstream speed is 6mph (with the current) and her upstream speed is 2mph (against the current). Use `d=rt ==> t=d/r` so the time required is the distance divided by the rate. So Emily's time for the course is the sum of the downstream and upstream legs. `t=6/6+6/2=1+3=4` so** Emily's course time is 4 hours.**

Ashley rows at 5mph. ` `Her downstream speed is 7mph and her upstream speed is 3mph. The time is

`t=6/7+6/3=2 6/7~~2.86` hours.

** Ashley's course time is 2.86 hours.**

**Ashley will complete her trip first by approximately 1.14 hours.** (1 hour and 8.4 minutes)