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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "Dana can run at a rate of speed four times faster than she can walk, but she can skip at a rate of speed that is half as fast as she can run. If she can skip at 3 miles per hour, how many miles can she travel in six hours if she spends one-third of the time running and two-thirds of the time walking?",
"answer": "If Dana can skip at half the speed she can run, then she can run at 3*2=<<3*2=6>>6 miles per hour.\nAnd since she can run at a speed that is 4 times faster than she can walk, this means she can walk at 6/4=1.5 miles per hour.\nIf two-thirds of the time is spent walking, then she walks for 6*(2/3)=<<6*(2/3)=4>>4 hours.\nIf one-third of the time is spent running, then she runs for 6-4=<<6-4=2>>2 hours.\nThus, she runs for 2 hours at 6 miles per hour, or 2*6=<<2*6=12>>12 miles.\nShe walks for 4 hours at 1.5 miles per hour, or 4*1.5=<<4*1.5=6>>6 miles.\nThus, altogether, she travels 12+6=<<12+6=18>>18 miles.\n#### 18",
"id_orig": 39,
"id_shuffled": 88,
"question_annotated": "{name,Dana} can run {mult_run,four} faster than she can walk, but she can skip at a rate of speed that is {frac_skip,half} as fast as she can run. If she can skip at {skip_speed,3} miles per hour, how many miles can she travel in {total_time,six} hours if she spends {frac_run,one-third} of the time running and {frac_walk,two-thirds} of the time walking?\n\n#init:\n- name = sample(names_female)\n- $mult_run = sample(multi_times)\n- $frac_skip = sample(fraction_alnum)\n- $skip_speed = range(2, 10)\n- $total_time = range(4, 12, 2)\n- $frac_run = sample(fraction_alnum)\n- $frac_walk = sample(fraction_alnum)\n\n#conditions:\n- frac_run + frac_walk == 1\n- skip_speed / frac_skip < 13\n- is_int(total_time * frac_walk * (skip_speed / frac_skip / mult_run))\n- is_int(skip_speed / frac_skip)\n- is_int(total_time * frac_run)\n- is_int(total_time * frac_walk)\n\n#answer: int((total_time * frac_run * (skip_speed / frac_skip)) + (total_time * frac_walk * (skip_speed / frac_skip / mult_run)))",
"answer_annotated": "If {name} can skip at {frac_skip} the speed she can run, then she can run at {skip_speed}*{1/frac_skip}=<<{skip_speed}*{1/frac_skip}={skip_speed / frac_skip}>>{skip_speed / frac_skip} miles per hour.\nAnd since she can run at a speed that is {mult_run} times faster than she can walk, this means she can walk at {skip_speed / frac_skip}/{mult_run}={skip_speed / frac_skip / mult_run} miles per hour.\nIf {frac_walk} of the time is spent walking, then she walks for {total_time}*{frac_walk}=<<{total_time}*{frac_walk}={total_time * frac_walk}>>{total_time * frac_walk} hours.\nIf {frac_run} of the time is spent running, then she runs for {total_time}-{total_time * frac_walk}=<<{total_time}-{total_time * frac_walk}={total_time * frac_run}>>{total_time * frac_run} hours.\nThus, she runs for {total_time * frac_run} hours at {skip_speed / frac_skip} miles per hour, or {total_time * frac_run}*{skip_speed / frac_skip}=<<{total_time * frac_run}*{skip_speed / frac_skip}={total_time * frac_run * (skip_speed / frac_skip)}>>{total_time * frac_run * (skip_speed / frac_skip)} miles.\nShe walks for {total_time * frac_walk} hours at {skip_speed / frac_skip / mult_run} miles per hour, or {total_time * frac_walk}*{skip_speed / frac_skip / mult_run}=<<{total_time * frac_walk}*{skip_speed / frac_skip / mult_run}={total_time * frac_walk * (skip_speed / frac_skip / mult_run)}>>{total_time * frac_walk * (skip_speed / frac_skip / mult_run)} miles.\nThus, altogether, she travels {total_time * frac_run * (skip_speed / frac_skip)}+{total_time * frac_walk * (skip_speed / frac_skip / mult_run)}=<<{total_time * frac_run * (skip_speed / frac_skip)}+{total_time * frac_walk * (skip_speed / frac_skip / mult_run)}={int((total_time * frac_run * (skip_speed / frac_skip)) + (total_time * frac_walk * (skip_speed / frac_skip / mult_run)))}>>{ int((total_time * frac_run * (skip_speed / frac_skip)) + (total_time * frac_walk * (skip_speed / frac_skip / mult_run)))} miles.\n#### {int((total_time * frac_run * (skip_speed / frac_skip)) + (total_time * frac_walk * (skip_speed / frac_skip / mult_run)))}"
}